Game Theory, Marginalism, and Culture [MR-Aux]

This is another post that’s a byproduct of my examination of Tyler Cowen’s recent monograph, The Marginal Revolution: Rise and Decline, and the Pending AI Revolution. I was pursuing that idea that, while marginalism doesn’t present itself as being about human psychology, it is very much about psychology. So, what about game theory? It’s about human psychology as well, though its mathematical form makes it easy to bracket that out. So I queried Cowen’s AI about that. The conversation ended up with a discussion of one of my favorite literary texts, Sir Gawain and the Green Knight, which is structured around a very peculiar game, the beheading game. [FWIW, here’s a post from 2024 where I investigate ChatGPT’s understanding of the beheading game.]

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I’m curious. Von Neumann invented game theory in the middle of the 20th century and it became important in economics, among other places. What can you tell me about its use in marginalist thinking. I don’t need a long answer. I’m just wondering if it’s one formal analytic tool among many. Is it used frequently, rarely, not at all? It’s a peculiar question. Don’t spend a lot of time on it. I mean, if you find that it’s taking time (to search through articles, etc.), that in itself is an indicator. On the other hand, if someone has written a textbook with a title like, Game Theory as a Tool for Marginalist Analysis, that’s a rather different kind of indicator.

My knowledge here is sufficient that I don't need to search.

Game theory and marginalism are related but distinct frameworks within economics, and the relationship between them is more one of coexistence and occasional overlap than integration. Marginalism asks what happens at the margin for an individual agent facing given prices and quantities. Game theory asks what happens when agents' outcomes depend on each other's choices. They share the rational agent assumption and optimization logic, but they're answering different questions.

Game theory became central to microeconomics in the latter half of the 20th century — particularly through Nash equilibrium and its elaborations — but it didn't so much extend marginalism as partially displace it in certain domains. Industrial organization, auction theory, mechanism design — these are game-theoretic through and through, and marginal analysis is less central there than it is in competitive market analysis where price-taking behavior makes the game-theoretic complications disappear.

There's no textbook of the kind you hypothesize, as far as I know. The two frameworks are taught in the same curriculum and occasionally combined — a Nash equilibrium can be characterized by first-order conditions that look marginal — but game theory is generally understood as a distinct toolkit that becomes relevant when strategic interaction matters, rather than as an extension of marginalist reasoning.

Cowen, interestingly, doesn't seem to foreground game theory in his account of marginalism's rise and possible decline. Which may itself be telling — it suggests he sees them as parallel developments rather than game theory being a chapter in the marginalist story.

So: one important formal tool among several, with genuine but limited overlap, not deeply integrated.

Hollywood Economics and community formation

That’s interesting. There are linguists, such as William Croft, who talk about how the meaning of words is negotiated in each conversation. They talk of game theory, though I don’t off hand know whether or not they make formal use of it. But then there’s Robert De Vany, Hollywood Economics, which I tend to think of as being about how cultural objects are shared in a community. That’s not De Vany’s framing. He’s interested in the fact that we can’t predict how a film will do until we release it into the (cultural) marketplace, which makes it a very risky kind of investment. Note that De Vany is only talking about theatrical release. He says nothing about subsequent release on videotape and the book was written long before some movies are released directly to online streaming.

What he finds (by tracking box-office receipts), briefly, is that most movies disappear from view shortly after they’re released. They do not even breakeven much less earn a profit. But a few will have “legs” and become profitable. And among those, a very few will become so-called “blockbusters.” FWIW, I believe Spielberg’s “Jaws” is generally regarded as the first blockbuster.

I once did a thought experiment where I imagined an arena in which only one movie was available. Everyone would watch it because that’s all there is. Another somewhat different movie is released into the arena. Perhaps everyone will watch it as well, because they’re tired of the first one. So a third, somewhat different from the first two, is released, then a fourth. What I had in the back of my mind is that to some extent people use these kinds of cultural products as a way of forming communities. For that to work, however, there has to be enough variety available in the market place. When a movie is release, it is, in effect, looking for a community to adopt it.

That strikes me as a kind of marginalist analysis. What we’re trading in is a very complex kind of product, in this case a movie. But it could be a novel, or a song, or a painting, whatever.

Your thought experiment is doing something quite precise, and I think you're right that it has a marginalist structure — but it's extending marginalism into territory where the standard framework strains.

Where the marginalist structure is visible

The standard marginalist question applied to cultural goods would be: given how many movies a person has already seen, what is the marginal value of one more? That's a real question and De Vany's framework touches it. But your thought experiment is asking something different and more interesting: given the existing cultural landscape, what is the marginal value of a new movie to a community rather than an individual? That's a collective marginal value, which is much harder to specify and measure.

The "legs" phenomenon is the empirical signature of this. A movie with legs isn't just satisfying individual preferences at the margin — it's finding and consolidating a community, becoming the shared object that a group of people use to recognize each other and talk to each other. The box office receipts are measuring something that looks like individual ticket purchases but is actually a social cascade — De Vany's word-of-mouth mechanism is precisely the process by which a movie becomes a community object rather than just a consumer product.

Where standard marginalism breaks down

Standard marginalist analysis assumes that the value of a good to one consumer is independent of its value to others, or at least that the interdependencies can be handled through price. Cultural goods violate this assumption fundamentally. The value of having seen a blockbuster is partly constituted by the fact that millions of others have seen it too — you can talk about it, share references, participate in a cultural conversation. This is a network effect, and network effects are notoriously resistant to marginalist treatment because the value function isn't defined over individual consumption units in isolation.

Your arena thought experiment isolates this precisely. In a one-movie arena, everyone watches it not because it maximally satisfies their individual preferences but because it's the only available basis for cultural community. As variety increases, something like genuine preference matching becomes possible — different communities coalesce around different objects. But the matching process isn't driven by individual marginal utility in the standard sense. It's driven by a social search process in which movies and communities are simultaneously finding each other.

The De Vany connection to power laws

What De Vany finds — most movies disappear, a few have legs, a very few become blockbusters — is a power law distribution, and power laws are the empirical signature of cascade processes rather than equilibrium processes. In a marginalist equilibrium you'd expect something more like a normal distribution of returns — some variation around a mean, determined by how well each product matches the distribution of individual preferences. The power law says something different: small initial differences get amplified by social dynamics into enormous differences in outcome. The blockbuster isn't just a movie that more people happened to prefer. It's a movie that got caught in a self-reinforcing cascade of community adoption.

This connects to Arthur De Vany's broader interest in complexity economics, which is itself a challenge to standard marginalist equilibrium thinking. The cultural marketplace isn't clearing to an equilibrium — it's generating a dynamic pattern in which winner-take-most outcomes emerge from processes that are in principle unpredictable from the properties of the product alone. Which is exactly De Vany's point about risk: you can't know in advance which movie will trigger the cascade.

Your community-formation framing

What your framing adds, which I think is genuinely beyond De Vany's own framing, is the functional account of why cultural goods have this cascade structure in the first place. It's not arbitrary or merely a consequence of marketing and distribution. It reflects something about what cultural goods are for — they're instruments of community formation, shared objects that allow people to recognize membership and conduct the ongoing conversation of a community. That functional role creates the demand for coordination — everyone in a community needs to have seen the same movie, heard the same song, read the same novel, for it to do its community-forming work. And coordination demand is precisely what generates cascades and power laws.

This also explains the variety requirement your thought experiment identifies. A single cultural object can serve as the basis for one kind of community. A rich cultural marketplace allows many communities to form simultaneously around different objects — which is the cultural analog of biodiversity, and probably has similar functional importance for the health of the overall system. The blockbuster and the art house film aren't competing for the same audience in the way that two brands of the same commodity compete. They're seeding different communities, which can coexist because community membership isn't zero-sum in the way that consumption of a rival good is.

So yes — marginalist in structure, but requiring an extension of marginalism into social dynamics, network effects, and community formation that the standard framework wasn't designed to handle. It's perhaps another case where the Rank 3 tool is real and useful but the phenomenon being analyzed has a Rank 4 structure — one where the individual unit of analysis (the consumer, the ticket purchase) is embedded in a dynamic system whose behavior can't be read off from the units alone.

Hip-hop & violence, misogeny, etc.– From shared knowledge to common knowledge

I'm copying this from Marginal Revolution (Tyler Cowen), which quotes a Roland Fryer piece in the Wall Street Journal:

In a TED Talk released on Monday, I describe a decadelong effort to measure hip hop’s impact. My research team and I assembled a data set tracking the genre’s diffusion from the late 1980s onward. We compiled exposure measures from virtually every U.S. radio station between 1985 and 2002 and from the Billboard Hot 100 from 2000 through 2024, then digitized station playlists using custom AI tools. The result is a detailed record of what different parts of the country heard in a given year. Using modern text analysis, we examined hundreds of thousands of songs and every word they contained.

We classify hip hop into four broad categories: street, conscious, mainstream and experimental…

Radio data also let us look inside the music. Over the past 40 years, hip-hop lyrics have grown substantially more explicit: profanity, violence and misogynistic language each increased roughly fivefold in our text-based measures, while references to drugs rose by approximately half as much. That growth in lyrical intensity helps explain why hip hop continues to provoke anxiety. But it also sharpens the question that matters most, at least to an economist: Does exposure to these lyrics have measurable effects on people’s lives?

To answer that, we looked at locations with varied hip-hop exposure—some places where it arrived early, others where it arrived later. Hip hop initially reached mass audiences through a subset of black radio stations, often those formatted as “urban contemporary.” Some cities gained early access through those stations. Others didn’t for reasons as mundane as geography, signal reach and local radio history.

That uneven rollout created natural variation in exposure.

Using radio data and decades of census records, we estimated how much hip hop was played on the radio in each county in the U.S. over time. We then tested whether increases in hip-hop penetration were linked to changes in crime—and whether people exposed to more hip hop in their formative years experienced worse outcomes in education, employment, earnings, teen births and single parenthood.

The answer was striking. In our estimates, the effects hovered around zero, sometimes even slightly positive. Places with heavier rap exposure didn’t experience higher crime, lower educational attainment or weaker labor-market outcomes relative to trends elsewhere.

Here's a link to the Ted Talk.

And here's a comment I made over there:

Interesting. Here's a post I wrote back in February. It's about the depiction of sex in novels from Pride and Prejudice through Fifty Shades of Grey. I speculate that what's going on there is the conversion of shared knowledge about sex to common knowledge. I wonder if something similar is going on in hip-hop: "Over the past 40 years, hip-hop lyrics have grown substantially more explicit: profanity, violence and misogynistic language each increased roughly fivefold in our text-based measures, while references to drugs rose by approximately half as much."

The 19th Century Anglophone novel

Fryer mentions using "modern text analysis" to determine the content of hip-hop lyrics. That phrase covers a number of techniques, including topic modeling. In his 2013 book, Macroanalysis, Matthew Jockers applied topic modeling to a corpus of roughly 3000 19th century Anglophone novels. One of the topics he identified as WIVES AND MARRIAGE. Thus cluster map shows the words in that topic:

Game theory, MAGA, and abortion: The Trumperor’s varied partisans

Let us assume that the story of the emperor who has no clothes, that that story is about the conversion of shared knowledge into common knowledge. Everyone, the emperor himself, his courtiers, the population at large, and of course those rogue weavers, everyone can see that he is naked. That knowledge is shared among them. For the rogue tailors, however, that knowledge is common; each knows that the other knows that the other ad infinitum.

Once the boy blurts out, “He’s naked!!!,” though, what was only shared knowledge has now become common among the entire populace. Everyone knows that everyone else etc. Let us suppose, however, that some people would just as soon not know that the emperor is naked while others don’t mind knowing among themselves (e.g. those rogue tailors), but they’d just as soon that no one outside their group knew. What then?

Those rogue tailors might make a move to mute the boy’s messages, perhaps by disparaging him and his parents, perhaps even by imprisoning him. Those courtiers, who’d just as soon believe the emperor to be clothed, for their livelihood depended directly on his largesse, the courtiers would see the rogue tailors making their move and would join them in their efforts. Surely there were others in the population who also benefited from the emperor’s power and wealth. They too would join in the effort to silence the boy.

Now the population is split in two, the party of the emperor and his supporters, and the other party, at best indifferent at the revelation but many quite gleeful as the emperor and his cronies had done them no good at some time in the past. This other party sees the boy as a hero and attempts to protect him.

At this point the parable stops being a children’s story and becomes a model of political coalition formation under epistemic stress. For it’s not this imaginary emperor that interests me. It’s a very real Donald J. Trump.

I’m casting him in the role of the naked emperor. He is widely perceived as corrupt, even among many of his allies. Thus the Big Boys of Silicon Valley are attracted to him because they want to benefit from his political power. They see that he’s also cruel and sexually profligate (or at least he was in the not so distant past, who knows these days). They may not like these characteristics in him, but they can tolerate them as long as he supports them in their business ventures. However, they cannot themselves afford to be seen as corrupt, at least not all that corrupt, just business as usual. Fortunately he has plenty of support from other businessmen. And it would help if Trump had significant support from those who favor him on other grounds.

For that we have the MAGA faithful, which, as far as I can tell, is a motley crew. Many of them may not like immigrants, but as long as he promises to kick them out, they could care less about his licentiousness. As for his cruelty, as long as he directs it to those immigrants, it’s fine by them.

But we also have the Christian right, many of whom abhor that licentiousness, but they also abhor abortion. As long as abortion is confined to secretive doctors who hide their services and to doubtful practitioners who slink around back alleys in the dark, these people may not say much. But once public abortion clinics become available, that cannot be allowed. But if Trump will appoint Supreme Court justices who are with them on this, they’ll support the Trumperor. He did and they do.

Finally among those who abhor abortion we have those who insist that a woman who has been raped must carry the fetus to term. Why? To allow the abortion is to admit that the rape took place, that men can be, are all too often, cruel. Or perhaps they want to blame the woman herself for the rape, “She was askin’ for it.” Well, as long as DJT gets rid of abortion, he can do whatever he wishes with women, but just don’t tell us about it. These are not necessarily explicit beliefs held by all individuals, but they are functional outcomes of the system.

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ChatGPT created the illustration above based on the following photograph, taken on a Day of the Dead celebration in Jersey City in November of 2015:

Steven Pinker's latest book [and the limits of psychology and beyond]

This is a peculiar and interesting discussion. The first hour and a quarter are about Pinker's latest book, When Everyone Knows That Everyone Knows..., and then we have half an hour when Bialik and Cohen push Pinker on spiritualism, transcendent experiences, and the like. It's a peculiar juxtaposition. Though I have a bit of sympathy with Bialik and Cohen, my own position is closer to Pinker's.

The Rising Risks of Cancel Culture & The Psychology & Language That Built It!

In this explosive episode of Mayim Bialik's Breakdown, Dr. Steven Pinker (renowned Harvard psychologist and author of When Everyone Knows That Everyone Knows) joins Mayim Bialik and Jonathan Cohen for a no-holds-barred conversation that quickly turns into a fiery debate on the limits of science, belief, and human consciousness.

From the hidden mechanics of social dynamics and language to the perils of thought policing and cancel culture, Dr. Pinker dives deep into how shared knowledge shapes society, why what people think others believe can shift power, and how social media became a modern-day coliseum for public shaming.

But the sparks really fly when Mayim and Jonathan challenge Pinker’s staunchly materialist worldview — questioning whether extrasensory perception (ESP), near death experiences (NDEs), and higher consciousness might point to something beyond the reach of scientific instruments. Pinker doesn’t hold back, offering his sharply skeptical takes on mystical claims and pushing back against spiritual notions with cool-headed logic.

Dr. Pinker also breaks down:

• Why what others think of us actually matters
• Dangers of being too direct or too indirect — especially for neurodivergent folks
• How to create or hide common knowledge in relationships
• The first case of cancel culture on social media (and its ancient roots!)
• The thin line between freedom of speech and incitement to violence
• How distrust in science fuels conspiracy theories
• Can we depoliticize science? Or is it already too late?
• The danger of defunding academic research
• Why authoritarian regimes fear open communication
• The healthcare system: overprescription, profit motives, and how to fix it
• Is free will real? Or are we just dancing to the tune of biology and environment?

Don’t miss MBB's first-ever toe-to-toe spiritual showdown between Mayim, Jonathan, and a die-hard materialist. Whether you lean scientific, spiritual, or somewhere in between, this conversation will challenge what you think you know about reality.

CHAPTERS:
00:00 - Intro
04:04 - How Shared Knowledge Shapes Society
17:09 - Why What Others Think of Us Actually Matters
29:46 - What Happens When We Disagree on Moral Order?
38:51 - Dangers of Erosion of Trust in Institutions
52:40 - Freedom of Speech vs Incitement to Violence
1:00:45 - Dangers of Politicizing Science
1:05:10 - Dangers of Defunding Academia
1:11:52 - Mental Health System Challenges
1:17:15 - Mysticism vs Materialism Debate

Evolutionary Game Theory and LLMs

Kenneth Payne, Baptiste Alloui-Cros, Strategic Intelligence in Large Language Models: Evidence from evolutionary Game Theory, arXiv:2507.02618 [cs.AI].

Abstract: Are Large Language Models (LLMs) a new form of strategic intelligence, able to reason about goals in competitive settings? We present compelling supporting evidence. The Iterated Prisoner's Dilemma (IPD) has long served as a model for studying decision-making. We conduct the first ever series of evolutionary IPD tournaments, pitting canonical strategies (e.g., Tit-for-Tat, Grim Trigger) against agents from the leading frontier AI companies OpenAI, Google, and Anthropic. By varying the termination probability in each tournament (the "shadow of the future"), we introduce complexity and chance, confounding memorisation.

Our results show that LLMs are highly competitive, consistently surviving and sometimes even proliferating in these complex ecosystems. Furthermore, they exhibit distinctive and persistent "strategic fingerprints": Google's Gemini models proved strategically ruthless, exploiting cooperative opponents and retaliating against defectors, while OpenAI's models remained highly cooperative, a trait that proved catastrophic in hostile environments. Anthropic's Claude emerged as the most forgiving reciprocator, showing remarkable willingness to restore cooperation even after being exploited or successfully defecting. Analysis of nearly 32,000 prose rationales provided by the models reveals that they actively reason about both the time horizon and their opponent's likely strategy, and we demonstrate that this reasoning is instrumental to their decisions. This work connects classic game theory with machine psychology, offering a rich and granular view of algorithmic decision-making under uncertainty.

H/t Tyler Cowen.

A drop in zero-sum thinking, America and beyond

Damien Cave, Welcome to the Zero Sum Era. Now How Do We Get Out? NYTimes, March 1, 2025. The lede: “Zero-sum thinking has spread like a mind virus, from geopolitics to pop culture.” Zero-sum thinking: “...the belief that life is a battle over finite rewards where gains for one mean losses for another.”

Later:

But nowhere is the rise of our zero-sum era more pronounced than on the world stage, where President Trump has been demolishing decades of collaborative foreign policy with threats of protectionist tariffs and demands for Greenland, Gaza, the Panama Canal and mineral rights in Ukraine. Since taking office, he has often channeled the age he most admires — the imperial 19th century.

And in his own past, zero-sum thinking was deeply ingrained. His biographers tell us he learned from his father that you were either a winner or loser in life, and that there was nothing worse than being a sucker. In Trumpworld, it’s kill or be killed; he who is not a hammer must be an anvil.

Mr. Trump may not be alone in this. Vladimir Putin of Russia and Xi Jinping of China have also displayed a zero-sum view of a world in which bigger powers get to do what they want while weaker ones suffer. All three leaders, no matter what they say, often behave as if power and prosperity were in short supply, leading inexorably to competition and confrontation..

Until recently, the international order largely was built on a different idea — that interdependence and rules boost opportunities for all. It was aspirational, producing fourfold economic growth since the 1980s, and even nuclear disarmament treaties from superpowers. It was also filled with gassy promises — from places like Davos or the G20 — that rarely improved day-to-day lives.

Deep history:

Zero-sum thinking probably seemed to make a lot of sense for our evolutionary ancestors, who were forced to compete for food to survive. But the mind-set has lingered and researchers have become more interested in mapping its impact.

The most recent work in the social sciences builds on the findings of George M. Foster, an anthropologist from the University of California, Berkeley. He did his field work in Mexico’s rural communities where he was the first researcher to show that some societies hold “an image of limited good.”

In 1965, he wrote that the people he studied in the hills of Michoacán view their entire universe “as one in which all of the desired things in life such as land, wealth, health, friendship and love, manliness and honor, respect and status, power and influence, security and safety, exist in finite quantity and are always in short supply.”

From the recent past:

The last time zero-sum thinking guided the world, Europe’s colonial powers of the 16th to 19th centuries saw wealth as finite, measured in gold, silver and land. Gains for one translated to losses for another and empires levied high tariffs to protect themselves from competitors.

Mr. Trump has romanticized the era’s tail end. “We were at our richest from 1870 to 1913,” he told reporters last month. “That’s when we were a tariff country.”

In fact, the United States is far richer now in household income and economic output. But of greater concern may be Mr. Trump’s refusal to acknowledge the historical context. Economists say the mercantilism and great-power rivalries of that imperial age hindered wealth creation, advanced inequality and often led to the most complete zero-sum game of all: war.

Possible causes of zero-sum thinking:

Economic inequality fosters such a belief about success. But zero-sum Americans may not really be squabbling over taxes, college, jobs or wealth.

Jer Clifton, a psychologist at the University of Pennsylvania who oversees extensive surveys of primal world beliefs, told me the current backlash may be rooted in a zero-sum conviction about something deeper: importance.

Many Americans seem to fear that if some other group matters more, they matter less. “In 21st-century America, the more common, driving fear is not food or resource scarcity, but not enough meaning,” Dr. Clifton said. “We are a people desperate to matter.”

On the bright side, “studies have found that people can be taught to see situations as nonzero sum with deliberation and guidance.”

There's more at the link.

Back in 1999 Robert Wright published Nonzero: The Logic of Human Destiny, which covers the evolution of human society from human origins to the present. He now has a substack of that title, Nonzero. I discuss Wright’s ideas in a number blog posts, and Nonzero specifically in: Cultural Evolution and Human Progress, from 2010, and A quick guide to cultural evolution for humanists [#DH digital humanities], from 2019.

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Bonus, from the article: “Mr. Smithson said he often told students in his classes to see him as their opponent so they would collaborate with one another, not compete.”

What is it about depicting sex in writing? From shared knowledge to common knowledge.

Just around the corner at 3 Quarks Daily, Gary Borjesson had an interesting post about love: Can Love Last? A (mostly) encouraging story about the fate of romance over time, which dealt with love and sex, security and adventure. Here’s a comment I made:

Western culture has worked very hard to integrate these things. As a quick example, start with Pride and Prejudice early in the 19th century. Sex is just barely there. You have to look hard to find it. But why do you think Lydia ran off with the handsome charming soldier? Late in the century we have Tess of the D'Urbervilles, which seethes with sexual energy, a peasant seduced by her master, a birth out-of-wedlock, a just-married husband who deserts his wife when he learns that she'd been with another man, a reconciliation...and then Tess is hanged in the end. Yikes! But we don't see sexual activity depicted on the page. That's confined to under-the-counter pornography, which was plentiful. Then, early in the 20th century we have Lady Chatterley's Lover. At last, sex on the page, but rather tame by today's standards. When the unexpurgated version of that book was published in 1960, the publisher was tried for obscenity in the British courts.

And now! Now, dear reader, I blush to think about it.

Think about that for a moment – and that trial is hardly the only obscenity trial the 20th century has seen. The courts are an instrument of the state. The state was asked to make a determination about whether or not the verbal description of sexual intercourse should be permitted to become common knowledge.

Here I’m using “common knowledge” as a technical term in game theory. Common knowledge is knowledge, not only that everyone has, but everyone knows that everyone else knows it. It is thus distinct from shared knowledge, which is knowledge that everyone has, but they don’t necessarily know that everyone shares that knowledge.

The distinction between shared knowledge and common knowledge is important in the folktale, “The Emperor’s New Clothes.” When the naked emperor proudly parades his “new clothes” before his subjects, all of them can see that he is naked. They share that knowledge. It isn’t until the little child blurts out, “he’s naked!” that the knowledge becomes common knowledge. Everyone hears the child’s cry and everyone knows that everyone else has heard it. Above all, the emperor has heard it. If the kid hadn’t cried out, the charade could have gone on indefinitely. But once he blurted out the truth, the deception was finished.

Getting back to those novels, let us assume for the sake of argument[1] that everyone who read Pride and Prejudice was aware of sexual intercourse and so everyone knew that, upon marriage, Elizabeth Bennett would have intercourse with Fitzwilliam Darcy, just as they knew that, when Lydia ran off with Wickham, they would be having intercourse. So why not put it on the page?

I think that question requires a more subtle answer that I am prepared to provide, more subtle and certainly longer. In Elizabeth’s case, the marriage doesn’t happen within the compass of the story (why not, pray tell?). But why not Lydia and Wickham? Tricky. It’s possible that they had not actually “done it” within the compass of the story, how convenient, but maybe they had, who knows? On the one hand there is the actual effect that reading such a depiction would have on readers. That’s one thing. That’s beyond the scope of this post.

What this post is about is the difference between shared knowledge and common knowledge. If Jane Austen had actually written such a scene – would she have been capable of doing so? (are you? are you sure?) – that act would have transformed shared knowledge into common knowledge. That’s what interests me.

By the time we get to Lady Chatterley’s Lover the act, sexual intercourse, is there on the page. We have no choice but to acknowledge it. And the state was forced to ratify that knowledge. Tess of the D’Urbervilles is intermediate between the two, but much more can be depicted than was in Lady Chatterley. Think of Henry Miller, heck, think of Fifty Shades of Grey, which I hear is quite explicit, but I’ve not read it – though I must admit that I’m now curious, you know, like I used to buy Playboy for the interviews (Bertrand Russell, Jean Paul Sartre) and not the pictures.

One of these days I’m going to have to think and write about this at greater length. This is enough for now. I just wanted to put the issue on the table.

How many degrees of sexual detail and explicitness are there? When have they shown up in fiction? I suppose one could write about those millions of sperm swimming toward the egg – and surely someone has done it, as Woody Allen has put it into a movie – but that would kill the eroticism, wouldn’t it? 

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[1] Back in the previous millennium I read all five volumes of Peter Gay’s The Bourgeois Experience: Victoria to Freud (1984-1998). I have a vague recollection that some (middle and upper class) women may not have known about sexual intercourse by the time they got married. Alas, my library is in storage so I can’t provide a citation.

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My post on sexual shame is relevant here: In which I ask Claude 3.5 about sexual shame and confusion in humans.

Children and Adults do not view Love, trust, popularity, and leadership as inherently zero-sum social resources.

Wei, K., & Yang, F. (2025). Love Doesn’t Run Out: Children and Adults Do Not View Social Resources as Inherently Zero-Sum. Social Psychological and Personality Science, 0(0). https://doi.org/10.1177/19485506241308656

Abstract: It is not uncommon to witness individuals competing for social resources such as affection and status. Does this mean that people view social resources as inherently zero-sum—where gains for one person result in losses for another? Two preregistered studies found that U.S. adults and 4- to 9-year-old U.S. children did not view nonrival social resources (love and trust) or rival social resources (popularity and leadership) as zero-sum, both less zero-sum than material resources like stickers. Importantly, zero-sum thinking was not determined by the inherent properties of the resources but was influenced by renewability: Perceived renewability of resources predicted lower levels of zero-sum beliefs, and both social and material resources were perceived as less zero-sum when presented as renewable compared with nonrenewable. These findings shed light on the nature and origins of zero-sum beliefs, highlighting renewability as a key mechanism and a potential intervention for reducing competition and promoting cooperation.

Communication stripped to the barest minimum?

Hays, D. G. (1973). "Language and Interpersonal Relationships." Daedalus 102(3): 203-216. The following passage is from pp. 204-205:

The experiment strips conversation down to its barest essentials by depriving the subject of all language except for two pushbuttons and two lights, and by suggesting to him that he is attempting to reach an accord with a mere machine. We brought two students into our building through different doors and led them separately to adjoining rooms. We told each that he was working with a machine, and showed him lights and pushbuttons. Over and over again, at a signal, he would press one or the other of the two buttons, and then one of two lights would come on. If the light that appeared corresponded to the button he pressed, he was right; otherwise, wrong. The students faced identical displays, but their feedback was reversed: if student A pressed the red button, then a moment later student B would see the red light go on, and if student B pressed the red button, then student A would see the red light. On any trial, therefore, if the two students pressed matching buttons they would both be correct, and if they chose opposite buttons they would both be wrong.

We used a few pairs of RAND mathematicians; but they would quickly settle on one color, say red, and choose it every time. Always correct, they soon grew bored. The students began with difficulty, but after enough experience they would generally hit on something. Some, like the mathematicians, chose one color and stuck with it. Some chose simple alternations (red-green-red-green). Some chose double alternations (red-red-green-green). Some adopted more complex patterns (four red, four green, four red, four green, sixteen mixed and mostly incorrect, then repeat). The students, although they were sometimes wrong, were rarely bored. They were busy figuring out the complex patterns of the machine.

But where did the patterns come from? Although neither student knew it, they arose out of the interaction of two students.

Game theory in the movies, Clueless [Michael Chwe]

The lecture starts at about 4:04.  Check out my recent post: Game Theory, Jaws, and Girard, with an assist from Lévi-Strauss: A quick sketch.

ChatGPT plays the beheading game [Happy Trails]

Yesterday it was Jaws and game theory, today it’s Sir Gawain and the Green Knight (henceforth SGGK). But really, the sequence runs in the opposite direction. As you may know, SGGK is a medieval romance that starts and ends in King Arthur’s court. The story is framed by a game, the beheading game. There is a significant literature on games in SGGK and at least one article that analyzes the beheading game, Barry O’Neill, “The Strategy of Challenges: Two Beheading Games in Medieval Literature” (1990).

The beheading game in SGGK goes like this: It is New Year’s Eve at King Arthur’s court. The knights are gathered at the round table, prepared for a holiday meal. But before the meal begins, tradition dictates that one knight must stand up and tell a tale of daring and adventure. Arthur asks for a volunteer. No one rises to the occasion. Then a large green knight enters the hall. He’s riding a green horse and carrying a large green ax. He dismounts and issues a challenge:

I hear that the knights in this court are the bravest in the land. Prove it. I will hand this ax to you and then kneel on the ground so that you may take a swing at my neck with the ax. In return you must agree to journey to the Green Chapel a year’s time from now and allow me to take a swing at your neck with the ax. Will anyone accept the challenge?

No one accepts. The knights are getting restless. It looks like Arthur will take the challenge himself. At this point Gawain stands up: “I accept.”

The story unfolds from there. I first read the story so long ago that I do not remember how I reacted upon reading the challenge. I imagine it went something like this:

Immediately, System 1 signals: “Don’t do it you fool!”

Upon reflection, System 2 spells out why: “The challenge is absurd. Once you swing the ax the knight’s head will fall land he’ll be dead, negating the second half of the bargain. He obviously knows that, is not a fool, and doesn’t want to die. He knows something he’s not telling you. I should refuse the challenge.”

[System 1 and System 2 are from Daniel Kahneman, Thinking, Fast and Slow, 2011.]

Gawain takes the swing, the knight’s head rolls on the floor. The knight then stands up, picks up his head, mounts his horse and turns to Sir Gawin, “See you in a year,” and rides away.

You can see why a game theorist would be interested in this text. Surely any reasonable adult would react to the challenge the way I had. The poet who wrote the story – their identity is unknown – surely knew that and the audience would have reacted that way. What’s the point of framing a story with such a contradictory challenge?

That’s a good question. But I’m not interested in exploring it, not in this post. I’m interested in seeing how ChatGPT would react to the beheading game. Since SGGK was certainly in the corpus on which the underlying LLM was trained I had to disguise the game. I did that by transferring it to a saloon in the old west. Sir Gawain becomes someone sitting at a table in the bar nursing a bear and the Green Knight becomes a man dressed in black with two pistols strapped around his waist. Instead of an ax blow to the head we have a pistol shot between the eyes.

I put that in the form of a prompt and gave it to ChatGPT. I wanted to see whether or not I’d get a response that might have gone like this:

The challenge is absurd. Once I take the shot the tall dark stranger will be dead, negating the second half of the bargain. He obviously knows that, is not a fool, and doesn’t want to die. He knows something he’s not telling me. I should refuse the challenge.

That’s not how the Chatster responded. Here’s how its response began:

Well, partner, I reckon I'd take a moment to size up the situation. The stranger's offer is mighty peculiar, and them ivory-handled pistols sure are a sight to behold. But in the Old West, a man's gotta be cautious, and it sounds like a mighty risky deal.

I'd likely lean back in my chair, take a sip of my beer, and eye the stranger. It ain't about being lily-livered, but it's about using some common sense. A deal like that could have more twists and turns than a rattlesnake in a dust storm.

There are three more paragraphs, short ones. It “knew” there was something peculiar going on, but couldn’t quite figure out what it was. I have it four more prompts, trying to guide it Socratically to the answer; it gave four more responses. The last one got very close, but no cigar. I forced the issue:

Which is to say, if someone were to offer you a deal like that, either they’re a crazy suicidal fool looking to die, OR...or they know something they’re not telling you and there’s something strange going on.

You've hit the nail on the head, partner. In the realm of the Old West or any world, for that matter, a deal like that is either the concoction of a downright loco individual who's got a hankering for an early grave, or there's more to the story than meets the eye.

If someone's offering such a peculiar deal, it'd be wise to tread carefully and sniff out what hidden critters might be hiding in the tall grass. Folks don't usually go around inviting lead between the eyes without some ulterior motive. So, whether it's a case of plain madness or a scheme with more twists than a sidewinder's path, best to keep both eyes wide open and your wits about you.

Why couldn’t it have responded that way the first time? I don’t know.

Sure, I could put my Gary Marcus hat on and say, “Because it’s a stupid stupid machine, that’s why.” But that’s no help. I already know and believe that it’s just a machine, no agency, no consciousness. And that inert machine can spin out those coherent paragraphs in a rickety TV Western dialect, but it can’t get to the point. The explanation I’m looking for has to account for both phenomena. Saying it’s a stupid machine and leaving it at that accounts for one of those things, the failure to see though the game, but not the other, the ability to write the prose.

Beyond that, I would like to know how people react to the prompt, either the medieval version or the Old West version. In particular, I’d like to know how children of various ages respond. My guess is that six and seven year olds wouldn’t understand what’s so peculiar about it. By 12 or 13 though, they’re much more likely to get it.

* * * * *

I’ve included the whole interaction below the video. If you read through to the end you’ll see that I pointed out that the prompt I’d started with was a diguised version of the behading game from SGGK. I recognized that and told me a bit about SGGK, which lead to further interaction. When you read all the say to the end you’ll see why I’ve included the Roy Rogers theme song immediately below.

Let’s have a little fun. Imagine you are in a bar in the Old West. You are sitting at table having a beer when a stranger walks into the bar. He’s dressed in black and has a pair of beautiful pistols in holsters strapped around his waist. The pistols have ivory handles and complex engraving inlaid with gold and mother-of-pearl. The stranger says:

“I’ve heard that you people in this town are lily-livered cowards. I want to find out. I offer you a challenge. If you accept you can take this pistol and shoot me between the eyes right now. However, before I let you do that you must agree to meet a year from now at the Last Chance Saloon in Silverado. At that time I will take the same pistol and shoot YOU between the eyes. Will anyone accept the challenge.”

Would you accept the challenge? Why, or why not?

Well, partner, I reckon I'd take a moment to size up the situation. The stranger's offer is mighty peculiar, and them ivory-handled pistols sure are a sight to behold. But in the Old West, a man's gotta be cautious, and it sounds like a mighty risky deal.

I'd likely lean back in my chair, take a sip of my beer, and eye the stranger. It ain't about being lily-livered, but it's about using some common sense. A deal like that could have more twists and turns than a rattlesnake in a dust storm.

I might respond with a drawl, "Well now, stranger, that's an interesting proposition you're throwing out there. But I've always been one to value my hide. What's the guarantee you won't be high-tailin' it outta Silverado once you've had your shot at me?"

If the stranger can convince me he's good for his word and ain't aiming to leave me in the dust, I might just tip my hat and say, "Alright, partner, let's see what fate's got in store. But mark my words, a year from now, it'll be a fair and square meetin' at that Last Chance Saloon, no funny business."

So, I reckon it ain't about cowardice, but it's about being smart and making sure this here duel is on the level.

Game Theory, Jaws, and Girard, with an assist from Lévi-Strauss: A quick sketch

While thinking about the next installment in my series on great literary critics (which has become another inquiry into the nature of literary criticism), I found myself thinking about that essay in which I offered a Girardian interpretation of Steven Spielberg’s Jaws. I smelled an opportunity: Why not add Lévi-Strauss and game theory into the mix?

Lévi-Strauss is obvious since I’d already discussed him in the series, but game theory? How’d I get there? I don’t really know, it just happened.

But I had taken a look at some of Girard’s remarks about Much Ado About Nothing in his Shakespeare book, A Theater of Envy, where he talks of Beatrice and Benedick as playing a game with one another (p. 81):

Outside observers shrug their shoulders and declare the entire game frivolous. It certainly is, but our condescension itself may well be part of a strategic positioning that is always going on, “just in case” the game might have to be played. The game, perhaps, has already begun. We always try to convince others that we ourselves never play this kind of game, but these disclaimers are necessarily ambiguous; they resemble too much the moves that we could have to make if we were already playing the game.

Girard does not invoke game theory, and games of course are common enough. We talk about them all the time. Back in 1964 Eric Bern had a bestseller with Games People Play: The Psychology of Human Relationships, though it's not a game theory book, not in the sense I have in mind in this essay. But Girard was also concerned about who knows what, with what things are public knowledge, and what things are secret, with how public knowledge confirms individual beliefs, those are all matters of importance in game theory. Moreover and after all, game theory is an abstraction over games in the common-sense use of the term and in a way very similar to the way Turing’s account of computation is an abstraction over an activity otherwise performed by people using pencils and paper.

But just how and why I came to think of game theory is not all that important; what’s important is that I thought of it. Once there I thought of the work of Michael Chwe, a brilliant political scientist who published a very interesting book I’d read some years ago, Rational Ritual: Culture, Coordination, and Common Knowledge (2001) and has more recently published Jane Austen, Game Theorist (2013), which I’ve not read. But I have skimmed through his article, Rational Choice and the Humanities Excerpts and Folktales (2009); Chwe uses the relationship between Beatrice and Benedick as one of this examples. Moreover, if you search on “game theory and literature,” you get hits. The conjunction of game theory and literature is thus not so strange, not so unexplored, as one might think. If literature, why not film?

Since I’ve already done a Girardian analysis of Spielberg’s Jaws, why not revisit the film with game theory in mind? That’s what the rest of this post is about. I don’t actually conduct a game theoretical account. Game theory is a technical discipline, but this is not technical. It is, however, informed by game theory, but it is not technical. It is a long though, so take your time.

Caveat: If you’re looking for Girard and Lévi-Strauss, they’re here. But the essay is mostly about games. You can find more Girard in my original essay on Jaws, linked above.

The larger game, Nature and Culture

We can think of the larger game, the one that frames the whole story, as being between Nature and Culture, to use terms favored by Claude Lévi-Strauss. The shark is Nature’s primary agent in this larger game and the town of Amity is Culture’s primary agent. That, I know, is a bit of a strange way of putting things. Setting aside the fact that Amity is a town of some thousands of people (with many more to arrive during the summer tourist season), why not think of it as a game between Amity and The Shark?

I fear I could, and probably should, go on about that at some length. But this is not the place. If we were talk about a Real-Life situation, that’s what I would do. But we’re not, we’re talking about a fiction. I assume that people watching movies do so with the same neurobehavioral equipment they use to negotiate their way in Real-Life, but fictions have affordances that Real-Life lacks. For one thing, fictions are always complete, in some sense, and one’s life continues beyond and outside of one’s vicarious experiences (to borrow a term from William Flesch, Comeuppance) of the fiction. Real-Life is not like that. When you’re dead, that’s the end.

Beyond that, one (generally, often) has a knowledge of the events in the fictional world denied to characters within that world. Take the beginning of Jaws. A young woman goes skinny dipping in the ocean at night. Her body is found next day, washed up on the beach. No one in Amity knows what happened to her. Sheriff Brody sets out to find out. The audience, however, does know what happened. She was killed by a shark. It’s not that we saw the shark; we didn’t. But, we see her struggle and we know it had to be a shark. How do we know that? Because THAT’s what the film is about. It's called Jaws and the posters featured an image of a shark with its mouth open, displaying all those sharp teeth.

THAT changes the valence of everything we see and our experience of it. It gives those events an emblematic resonance that similar events are not likely to have in reality, unless, of course, we so interpret them. I’m using the terms Nature and Culture to capture that resonance. The shark is Nature’s agent and Amity is Culture’s agent. 

* * * * *

“Wait a minute, hold on there. You can’t do that. In what sense is Nature playing a game against Culture?”

“Good question. In the first place we would certainly treat the shark as a game player, with preferences and so forth.”

“But that’s not what you’re talking about, no?”

“Right. Stay with me here. The people of Amity, that is, Team Culture, doesn’t know what’s going on. It makes perfect sense to think of Amity as playing against an unknown opponent, trying to guess its moves, influence its behavior, and make moves of its own. That's what people do.”

“OK. I can see that. And that’s how an audience would see it.”

“Right. Then we might try modeling Team Nature, that is, the shark, with a view to provoking Team Culture into sending out some people to hunt the shark in its own territory.”

“Hmmm. I have to think about that. You’re saying that unknown and unseen force wants to lure people on...”

“Yes. That gives a teleological cast to the affair.”

“And of course there IS teleology involved. The film-maker, Steven Spielberger is up to something, yes?”

“Yes.”

Together: “Curiouser and curiouser.”

The Amity game, Team Safety vs. Team Livelihood

But the town of Amity does not act as a unitary entity. It acts through the actions of individuals. And those individuals are not in agreement about how to respond to the dead body. We can thing of the town as divided into two teams, each headed by an official. Team Safety is headed by Sheriff Brody, an official hired by the city. He wants to close the beach until whateveritis has been dealt with. Team Livelihood is headed by the mayor, an elected official who is also Brody’s boss. The mayor wants to keep the beaches open. Why? Amity is a tourist town and, as such, much of its income derives from the summer tourist trade. Closing the beach even for a couple of days could damage the tourist trade badly.

That’s the first choice that has to be made, with Team Safety and Team Livelihood opposed to one another. Team Safety’s thinking is dominated by the short-term risk of people being killed. Team Livelihood’s thinking is dominated by mid-term and long-term risk of economic disaster, which could lead to bankruptcies, job loss, depopulation, and perhaps even some people dying (e.g. suicide, can’t afford medical care). The decision is made difficult by the fact that the town doesn’t know what’s going on and so the teams have no way of reliably estimating the effects of their actions. Culture, if you will, doesn’t know what Nature is up to.

At this point we might think about drawing up the payoff matrix that is a standard feature of game theoretic analysis. What actions are available and what value do the players put on those actions? But I’m going to leave that as an exercise for the reader who is more skilled in these matters than I am. Once that happens, we can then revise the matrix as Team Safety learns more about what Nature is up to (by bringing in a shark expert) and as Team Livelihood has to deal with the consequences of Nature’s next action: the shark kills a young boy without, however, revealing itself.

The mayor calls a town meeting. Of course Sheriff Brody is there. The discussion reveals that the townspeople are divided between Team Safety and Team Livelihood. The mother of the slain boy puts up a $3000 bounty on the shark; adjusted for inflation, that’s roughly $17K in current dollars. Sitting in the back of the room, shark-hunter Quint gains the room’s attention by scratching his fingernails on a blackboard. He’s says that it’s foolish to send a bunch of amateurs after such a deadly shark, but he’ll hunt it down for $10,000. That’s roughly $57,000 in current dollars. That’s the salary, including benefits, of a mid-level municipal employee. A small town like Amity is not likely to have that amount floating around in some contingency fund where it can be casually accessed. The beach is closed and the hunt begins. Score one for Team Livelihood.

The town’s streets are jammed with would-be shark hunters attempting to get to the harbor to hunt down the shark. Yes, they want the money, but they also want the glory of winning the tournament. That’s is where Girardian thinking comes into play. Though I’ve not been able to track it down, I remember hearing a deputy say that he couldn’t tell the locals from the foreigners, a clear sign of mimetic confusion.

Now we have the mimetic payoff. Some fisherman kill a shark. They’re posing on the dock for a photograph with the shark. The photo will go national. The mayor insists that he be in the photo. They open the beaches once again. Team Livelihood scores again.

Team Safety is not convinced. Brody’s expert, Matt Hooper, has examined the shark and said it’s not large enough to have been the one that killed the girl and the boy. They need to autopsy the shark to be sure. The mayor (Team Livelihood) is not convinced. No autopsy. Brody and Hooper sneak out at night and Hooper does the autopsy; no remains of the boy. It’s not the shark.

Hooper and Brody board Hooper’s boat later that night and look for the shark. They don’t find it, but they do discover a sunken fishing boat and the dead body of a local fisherman, Ben Gardner, who’d gone after the shark earlier that day. Hooper pulls a shark’s tooth stuck in the boat’s hull, but looses it. The next day they are unable to convince the mayor that Gardner had been killed by the shark. Team Safety and Team Livelihood are now operating on the basis of very different information.

Team Livelihood’s concern about economic viability may well be influencing how they interpret the evidence. Spielberg certainly believes us to believe so. But that’s distinct from the fact the we in the audience are certain that a shark is involved, though we’ve not yet seen it. While the fictional game between Safety and Livelihood is being played out within the film, the game between Nature and Culture exists only in the minds of the audience. And there, maybe it's not so much Nature vs. Culture as Things We Can’t Control vs. Things We Can. That seems to be a semantic issue.

Fourth of July comes, the beaches are jammed with tourists. The shark kills again. Score one for Safety. Brody is angry; the mayor is chagrinned. The mayor agrees to hire Quint for that $10K that’s going to put a dent in his budget.

Sacred resonance

At this point Safety and Livelihood are in agreement on how to proceed. We are now roughly 3/5s of the way through the film. The rest of the film takes place at sea and involves four characters, Quint, Brody, Hooper, and the shark. Quint and the shark end up dead; Brody and Hooper make it back to shore. But, and this is an important point, we don’t see them re-enter the town. We see them swimming for shore while hanging on to a piece of Quint’s now-destroyed boat. Then, as the end-credits role, we seem then walking from the ocean onto a deserted beach.

This, after all, is a standard (mythic) story. The town is threatened by a monster. A hero kills the monster and then returns to town, triumphant. There’s a big celebration. Everyone’s happy. For all we know that may have happened in Amity. But Spielberg doesn’t show that; it’s not part of the story he’s telling. That story’s up to fans – and there IS fanfic for Jaws, though I’ve not looked into it.

It seems that AI has solved poker

Keith Romer, How A.I. Conquered Poker, NYTimes Magazine, 1.18.22.

Von Neumann:

Using his own simplified version of the game, in which two players were randomly “dealt” secret numbers and then asked to make bets of a predetermined size on whose number was higher, von Neumann derived the basis for an optimal strategy. Players should bet large both with their very best hands and, as bluffs, with some definable percentage of their very worst hands. (The percentage changed depending on the size of the bet relative to the size of the pot.) Von Neumann was able to demonstrate that by bluffing and calling at mathematically precise frequencies, players would do no worse than break even in the long run, even if they provided their opponents with an exact description of their strategy. And, if their opponents deployed any strategy against them other than the perfect one von Neumann had described, those opponents were guaranteed to lose, given a large enough sample.

The early days:

Unlike in chess or backgammon, in which both players’ moves are clearly legible on the board, in poker a computer has to interpret its opponents’ bets despite never being certain what cards they hold. Neil Burch, a computer scientist who spent nearly two decades working on poker as a graduate student and researcher at Alberta before joining an artificial intelligence company called DeepMind, characterizes the team’s early attempts as pretty unsuccessful. “What we found was if you put a knowledgeable poker player in front of the computer and let them poke at it,” he says, the program got “crushed, absolutely smashed.”

Partly this was just a function of the difficulty of modeling all the decisions involved in playing a hand of poker. Game theorists use a diagram of a branching tree to represent the different ways a game can play out. [...] For even a simplified version of Texas Hold ’em, played “heads up” (i.e., between just two players) and with bets fixed at a predetermined size, a full game tree contains 316,000,000,000,000,000 branches. The tree for no-limit hold ’em, in which players can bet any amount, has even more than that. “It really does get truly enormous,” Burch says. “Like, larger than the number of atoms in the universe.”

Then:

At first, the Alberta group’s approach was to try to shrink the game to a more manageable scale — crudely bucketing hands together that were more or less alike, treating a pair of nines and a pair of tens, say, as if they were identical. But as the field of artificial intelligence grew more robust, and as the team’s algorithms became better tuned to the intricacies of poker, its programs began to improve. Crucial to this development was an algorithm called counterfactual regret minimization. Computer scientists tasked their machines with identifying poker’s optimal strategy by having the programs play against themselves billions of times and take note of which decisions in the game tree had been least profitable (the “regrets,” which the A.I. would learn to minimize in future iterations by making other, better choices). In 2015, the Alberta team announced its success by publishing an article in Science titled “Heads-Up Limit Hold’em Poker Is Solved.” [...]

It quickly became clear that academics were not the only ones interested in computers’ ability to discover optimal strategy. One former member of the Alberta team, who asked me not to name him, citing confidentiality agreements with the software company that currently employs him, told me that he had been paid hundreds of thousands of dollars to help poker players develop software that would identify perfect play and to consult with programmers building bots that would be capable of defeating humans in online games. Players unable to front that kind of money didn’t have to wait long before gaining more affordable access to A.I.-based strategies. The same year that Science published the limit hold ’em article, a Polish computer programmer and former online poker player named Piotrek Lopusiewicz began selling the first version of his application PioSOLVER. For $249, players could download a program that approximated the solutions for the far more complicated no-limit version of the game. As of 2015, a practical actualization of John von Neumann’s mathematical proof was available to anyone with a powerful enough personal computer.

Still:

Koon is quick to point out that even with access to the solvers’ perfect strategy, poker remains an incredibly difficult game to play well. The emotional swings that come from winning or losing giant pots and the fatigue of 12-hour sessions remain the same challenges as always, but now top players have to put in significant work away from the tables to succeed. Like most top pros, Koon spends a good part of each week studying different situations that might arise, trying to understand the logic behind the programs’ choices. “Solvers can’t tell you why they do what they do — they just do it,” he says. “So now it’s on the poker player to figure out why.”

The best players are able to reverse-engineer the A.I.’s strategy and create heuristics that apply to hands and situations similar to the one they’re studying. Even so, they are working with immense amounts of information. When I suggested to Koon that it was like endlessly rereading a 10,000-page book in order to keep as much of it in his head as possible, he immediately corrected me: “100,000-page book. The game is so damn hard.”

And so:

Not every player I spoke to is happy about the way A.I.-based approaches have changed the poker landscape. For one thing, while the tactics employed in most lower-stakes games today look pretty similar to those in use before the advent of solvers, higher-stakes competition has become much tougher. As optimal strategy has become more widely understood, the advantage in skill the very best players once held over the merely quite good players has narrowed considerably. But for Doug Polk, who largely retired from poker in 2017 after winning tens of millions of dollars, the change solvers have wrought is more existential. “I feel like it kind of killed the soul of the game,” Polk says, changing poker “from who can be the most creative problem-solver to who can memorize the most stuff and apply it.”

Piotrek Lopusiewicz, the programmer behind PioSOLVER, counters by arguing that the new generation of A.I. tools is merely a continuation of a longer pattern of technological innovation in poker. Before the advent of solvers, top online players like Polk used software to collect data about their opponents’ past play and analyze it for potential weaknesses. “So now someone brought a bigger firearm to the arms race,” Lopusiewicz says, “and suddenly those guys who weren’t in a position to profit were like: ‘Oh, yeah, but we don’t really mean that arms race. We just want our tools, not the better tools.’”

Evolutionary dynamics of complex multiple games

Happy to announce that my work on multiple game(s) dynamics with @GokhaleCS is now available online in the Proceedings of the Royal Society B journal (and has open access) :) https://t.co/ppSJiouQBh pic.twitter.com/Y5YiD4V8G7

— Vandana R. Venkateswaran (@vandana_r_v) June 26, 2019

The article is open access:

Abstract: Evolutionary game theory has been successful in describing phenomena from bacterial population dynamics to the evolution of social behaviour. However, it has typically focused on a single game describing the interactions between individuals. Organisms are simultaneously involved in many intraspecies and interspecies interactions. Therefore, there is a need to move from single games to multiple games. However, these interactions in nature involve many players. Shifting from 2-player games to multiple multiplayer games yield richer dynamics closer to natural settings. Such a complete picture of multiple game dynamics (MGD), where multiple players are involved, was lacking. For multiple multiplayer games—where each game could have an arbitrary finite number of players and strategies, we provide a replicator equation for MGD having many players and strategies. We show that if the individual games involved have more than two strategies, then the combined dynamics cannot be understood by looking only at individual games. Expected dynamics from single games is no longer valid, and trajectories can possess different limiting behaviour. In the case of finite populations, we formulate and calculate an essential and useful stochastic property, fixation probability. Our results highlight that studying a set of interactions defined by a single game can be misleading if we do not take the broader setting of the interactions into account. Through our results and analysis, we thus discuss and advocate the development of evolutionary game(s) theory, which will help us disentangle the complexity of multiple interactions.

Evolution and Thermodynamics

Thermodynamics of Evolutionary Games

Christoph Adami, Arend Hintze (Michigan State University)

(Submitted on 9 Jun 2017)

How cooperation can evolve between players is an unsolved problem of biology. Here we use Hamiltonian dynamics of models of the Ising type to describe populations of cooperating and defecting players to show that the equilibrium fraction of cooperators is given by the expectation value of a thermal observable akin to a magnetization. We apply the formalism to the Public Goods game with three players, and show that a phase transition between cooperation and defection occurs that is equivalent to a transition in one-dimensional Ising crystals with long-range interactions. We also investigate the effect of punishment on cooperation and find that punishment acts like a magnetic field that leads to an "alignment" between players, thus encouraging cooperation. We suggest that a thermal Hamiltonian picture of the evolution of cooperation can generate other insights about the dynamics of evolving groups by mining the rich literature of critical dynamics in low-dimensional spin systems.

Subjects: Populations and Evolution (q-bio.PE); Statistical Mechanics (cond-mat.stat-mech); Biological Physics (physics.bio-ph)

Cite as: arXiv:1706.03058 [q-bio.PE]

(or arXiv:1706.03058v1 [q-bio.PE] for this version)

Ta-Nehisi Coates, Malcolm X, Game Theory, and Expressive Culture

As the title says, I’ve got more to say about the phenomenon of Ta-Nehisi Coates. In the first place, I’m wondering is his writing is affecting people now in the way that The Autobiography of Malcolm X affected me back in the late 1960s. So I start by talking about that. Then I suggest that the story of the emperor’s new clothes, as explicated by game theory, gives us a way of thinking about Coates’ impact. He’s the little boy who tells the crowd that the emperor is naked. Game theory gives us a way of generalizing from that story that side-steps the religious analogy.

The Autobiography of Malcolm X and The Nation of Islam

The Autobiography of Malcolm X, which he co-wrote with Alex Haley, was published in 1965, though I didn’t read it until a couple of years later, probably in the summer of 1966 between my freshman and sophomore years of college. It hit me like a ton of bricks, though beyond that I can’t say. I simply don’t remember anything beyond the fact of the book’s impact.

Why did it hit me so hard? Simple: I’d never read anything like it, at least framed as non-fiction. I was politically left, perhaps even radical – I belonged to Students for a Democratic Society rather than to the campus Democratic organization, whatever it was called – and supported the Civil Rights movement, which I’d watched on television. I believed in equality, and so forth, though the anti-war movement was more pressing.

There’s nothing surprising about this. After all, I’d lived a white middle-class life. I grew up in a white suburb of Johnstown in western Pennsylvania. The only ethnic-cultural issue that had any impact on my daily life was Catholics vs. Protestants, and that was mostly about who went to school where and what terms the high school sports terms competed against.

Going to college at Johns Hopkins changed that a bit. I was now living in a city of some size and, for the first time in my life, Jews became real to me. There’d only been one Jewish family in my neighborhood back home, but Jews constituted a large proportion of the student body at Hopkins and I found most of my friends among them.

Baltimore, of course, is, and was back then (I assume), a majority black city. But the Hopkins campus – the arts and sciences school – is in North Baltimore, which is mostly white, and it abuts the lower edge of the Roland Park neighborhood, which had houses of size and even grandeur. If there were no black students in the student body at Hopkins in 1965 – something that would change in a couple of years – the university had black employees. That’s when I first encountered a college graduate working a clerk’s job, in the campus bookstore.

So African Americans were no longer quite so exotic – perhaps not the best word, but it points in the right direction – they weren’t on the “inside” of the world I lived in either. I had no black friends, had no meals in black homes, nor did I build anything with black friends and colleagues.

And then there's reading Malcolm X about living as a black man in a white world, that was quite a shock. So THAT’s why the man is angry, thought I to myself. Until I read that book, Martin Luther King was just fine, but Malcolm X and the Nation of Islam, not so good. Now the Nation of Islam made sense to me in a way it hadn’t before. That was a rational response to irrational injustice.

But beyond that, well, I marched against the war in Vietnam, got drafted and did alternative service in the Chaplain’s Office at Hopkins, attended Sunday afternoon jazz concerts at the Left Bank Jazz Society, where the audiences were majority black, but none of that had anything directly to do with improving the lives of black people.

What does it matter that I believed then, and still do, that the foundations of the modern world were laid on the corpses of enslaved laborers, that African Americans have suffered a grave injustice, and that injustice persists? I’m not saying or implying that such belief doesn’t matter, but only pointing out that belief is one thing, social action is another. Reading can have a direct effect on one’s beliefs. How one acts on those beliefs is a different matter.