Vizzinni: But it’s so simple. All I have to do is divine from what I know of you. Are you the sort of man who would put the poison into his own goblet, or his enemy’s? Now, a clever man would put the poison into his own goblet, because he would know that only a great fool would reach for what he was given. I’m not a great fool, so I can clearly not choose the wine in front of you. But you must have known I was not a great fool; you would have counted on it, so I can clearly not choose the wine in front of me!
Man in Black: You’ve made your decision then?
Vizzini: Not remotely!
Several of the books I have read over the last few months offer different perspectives on a fascinating study. The study, conducted by a joint team from Kyoto University and Caltech, pitted chimpanzees and humans against each other in a game of strategy that game theorists have dubbed ‘Matching Pennies.’ In his book The Secret of Our Success (which I sorta reviewed here), anthropologist Joseph Henrich explains both how the game works and how the chimps did:
Matching Pennies is a classic game of strategic conflict that has been played with both chimpanzees and humans. In the game, individuals are paired with another of their species for several rounds of interaction. Each player is placed into the role of either the Matcher or the Mismatcher. In each round, participants must select either Left or Right. The Matcher gets a reward only when his choice (Left or Right) matches the choice of his opponent. By contrast, the Mismatcher gets a reward only when his choice mismatches his opponent. The rewards, however, need not be symmetric, as illustrated in figure 2.4. In this asymmetric version, the Matcher gets 4 apple cubes (or cash for humans) when she successfully matches on Left, but only gets 1 cube when she matches on Right. Meanwhile, the Mismatcher gets only two cubes for any successful mismatches, no matter how they arise.
This kind of interaction can be analyzed using game theory. To win, the first thing to realize is that both players should be as unpredictable as possible. Nothing about your prior choices should allow your opponent to anticipate your next play—you have to randomize. To see this, put yourself into the shoes of the Matcher. Your opponent gets two cubes whether he plays Left (L) or Right (R), so you should essentially flip a coin with heads for R and tails for L. This means you’ll play R and L each 50% of the time, and your opponent won’t be able to predict your choices. If you deviate from 50%, your opponent will be able to exploit you more frequently. Now consider matters from the position of the Mismatcher: if you now similarly flip a coin, the Matcher will shift to play mostly L, since that gives him four instead of one. To compensate, as a Mismatcher you need to play R 80% of the time. Thus, the predicted winning strategy in a contest of intelligent rational actors is that Matchers should randomize their responses, playing L 50% of the time, while Mismatchers should randomize by playing L only 20% of the time. This outcome is called the Nash equilibrium. The fraction of the time that one should play L can be moved around by simply changing the payoffs for matching or mismatching on L or R.
A research team from Caltech and Kyoto University tested six chimpanzees and two groups of human adults: Japanese undergraduates and Africans from Bossou, in the Republic of Guinea. When chimpanzees played this asymmetric variant of Matching Pennies (figure 2.4), they zoomed right in on the predicted result, the Nash equilibrium. Humans, however, systematically and consistently missed the rational predictions, with Mismatchers performing particularly poorly. This deviation from “rationality,” though it was in line with many prior tests of human rationality, was nearly seven times greater than the chimpanzees’ deviation. Moreover, detailed analyses of the patterns of responses over many rounds of play show that the chimps responded more quickly to both their opponents’ recent moves and to changes in their payoffs (i.e., when they switched from playing the Matcher to the Mismatcher). Chimpanzees seem to be better at individual learning and strategic anticipation, at least in this game.
The performance of the apes in this setup was no fluke. The Caltech-Kyoto team also ran two other versions of the game, each with different payoffs. In both versions, the chimps zeroed in on the Nash equilibrium as it moved around from game to game. This means that chimps can develop what game theorists call a mixed strategy, which requires them to randomize their behavior around a certain probability. Humans, however, often struggle with this. A final insight into the humans’ poor performance comes from an analysis of participants’ response times, which measures the time from the start of a round until the player selects his move. For both species, Mismatchers took longer than Matchers. However, the humans took much longer than the chimps. It’s as if the humans were struggling to inhibit or suppress an automatic reaction.
The chimpanzees are better strategists than the humans are. But why? The authors of the study suggest that development of language skills and stronger executive function in human brains has forced a trade off:
Matsuzawa hypothesizes that chimpanzees are better than humans at the masking memory task because human evolution degraded certain memory skills to make room in the brain for development of human language-related skills. The notion that chimpanzees may display some superior cognitive abilities due to a suggested lack of interference from language-related processes is further supported by evidence from comparative eye-tracking studies. These studies have shown that chimpanzees foveate on the same pictorial elements as humans, but do so in less time by making quicker eye movements. Authors suggest that longer fixation patterns displayed by humans are caused by high-level semantic processing on objects as they are viewed, and that the relative lack of such kinds of language processing in chimpanzees gives them an advantage for making rapid perceptual assessments of visual scenery.
The relatively poor performance of humans, together with the conjectured importance of language for humans, raise issues about the relevance of those game theory experiments in which humans have traditionally been unable to talk to each other. If verbal communication is indeed key to human strategic interaction, it seems that external validity would be enhanced if one lets humans talk.
Henrich has an alternate explanation, arguing that human strategy-crafting can be distorted by an inborn drive to imitate:
This pattern may reflect a broader bug in human cognition: our automatic and unconscious tendency to imitate (to match). In Matching Pennies and other games like Rock-Paper-Scissors, one player sometimes accidentally reveals his or her choice a split-second before the other player. This flash look at an opponents’ move could result in more victories for those who delay. And in Matching Pennies, experiments show that it does for Matchers, for whom copying leads to victories. For Mismatchers, however, it leads to more losses, because they sometimes fail to inhibit imitation. In Rock-Paper-Scissors, it results in more ties (e.g., rock-rock), because the slower player sometimes unconsciously imitates the choice of his or her opponent. The reason is that we humans are rather inclined to copy—spontaneously, automatically, and often unconsciously. Chimpanzees don’t appear to suffer from this cognitive “bug,” at least not nearly to the same degree. 
I do not find Henrich’s hypothesis convincing. His main point in this chapter is that human rationality is not nearly as neat as we think it is: after all, the Chimpanzees out perform us in many cognitive tasks, including this one. The “secret of our [read: humanity’s] success” is not our biologically inherited capacity for reason, but the blindly evolved set of practices and beliefs that we have culturally inherited. Key to this argument is the notion that humans are especially prone to imitation. Compulsive and accurate imitation is what makes cultural evolution and inheritance possible.
The trouble with this view is that there is very little evidence that humans are actually compulsive imitators. Olivier Morin devotes several chapters to this topic in his book How Traditions Live or Die. Morin argues that cultural evolutionists like Henrich are wrong. The evidence on imitation, Morin points out, all goes in the opposite direction: humans are finicky imitators. We imitate very little of what we encounter, almost always do so as the result of careful calculation (not blind instinct), and are not skillful in our imitations. Morin maintains that the chapters of evidence he has mustered for this assault on cultural evolution is enough to debunk most of the theory altogether. I disagree (at some point I will have to review his book), but I do think the evidence he has collected debunks this particular explanation for the Machiavellian chimp.
What then explains the chimpanzee’s strategic acumen? My favored explanation was proposed by Kenneth Payne in his book Strategy, Evolution, and War: From Apes to AI (which I reviewed here). He suggests that humans have trouble locating the Nash Equilibrium in competitive contests like these because they have been beguiled by intentionality (also known as “theory of mind“):
Why did the humans fare worse? The study’s authors speculated that human capacity for language and categorization had been earned at the expense of pattern recognition and perception, at which the chimpanzees remained adept. This is possible, though it does take a rather zero-sum view of cognitive abilities. I would highlight instead another uniquely human capability-intentionality-as the likely culprit. The human players were trying to put themselves inside the mind of their adversaries. That is, humans were strategizing on the basis of mind reading and not on the basis of probabilities and payoffs. Language and categorization are certainly important features of human cognition in which they surpass other primates (especially when it comes to the categorization of abstract meanings). but they are also manifestations of our intense sociability-the bedrock of which is our sense of others as autonomous agents with their own perceptions and beliefs. So strong is this sense of the inner lives of others that we cannot switch it off and engage in an alternative, more mathematically rational approach to strategy.
What might humans gain from being worse than chimps at finding an optimum strategy in adversarial games like this? The answer lies in the intense sociability of humans, even compared to the obviously social world of their fellow primates. Our theory of mind is the basis of rich cooperative relationships within human society. Being good at cooperating-understanding intentionality and communicating through language-has allowed our group sizes to expand and to forge mutually advantageous relationships on the basis of trust and comparative advantage. As individuals we may not outperform chimpanzees in the narrow ordered universe of two-person strategy games, but then those games differ from many of the real challenges in the social world of humans, where cooperation for mutual gain rather than zero-sum antagonistic relationships are typical. 
For millennia humans have celebrated what we now call ‘theory of mind’ as keystone of strategic brilliance. The master politician outmaneuvers his opponents by anticipating what they will think before they think it. Like Zhuge Liang, the master strategist wins his victories on the mental plane:
Payne’s view of strategic decision is less romantic. Our theory of mind makes us more empathetic and cooperative, not more Machiavellian. Each attempt to peer into an opponent’s brain is an exercise in self-deception. Like Vizzinni in the Princess Bride, humans are ever beguiled into believing they have won the battle of wits. Too late do they discover that the best Machiavellians are not mind-readers.
 Joseph Henrich, The Secret of Our Success: How Culture Is Driving Human Evolution, Domesticating Our Species, and Making Us Smarter (Princeton: Princeton University Press, 2016), 80-81.
 Christopher Flynn Martin, Rahul Bhui, Peter Bossaerts, Tetsuro Matsuzawa, and Colin Camerer, “Chimpanzee choice rates in competitive games match equilibrium game theory predictions,”
Nature: Scientific Reports, vol 4, #5182 (2014).
 Henrich, Secret of Our Success, 81.
 Olivier Morin, How Traditions Live and Die (Oxford: Oxford University Press, 2015), 53-120.
 Kenneth Payne, Strategy, Evolution, and War: From Apes to AI (Washington, D.C.: Georgetown University Press, 2018), 51.