Brian Skyrms is one of the few philosophers who has been elected to the National Academy of Sciences of the United States. He is an outstanding example of what seems to me to be a trend in modern philosophy of science, which is to learn the relevant scientific practices thoroughly so that one's contribution as a philosopher is at a high technical level of expertise. This book is accessible to the interested non-professional, but the journal articles on which it is based are quite sophisticated. I am not sure whether we should consider Skyrms' ideas as contribution to social theory, social philosophy, or both.  Then again, perhaps it doesn't matter.Skyrms' preferred method is to take a simple two-player game like the stag hunt or the prisoner's dilemma and explore the implications of repeating the game, playing it on a lattice, allowing player strategies to evolve, and otherwise enriching the game's structure to better approximate some forms of real social interaction. Skyrms is above all an explorer rather than an exhaustive taxonomist. He wanders through the forest of exotic plausible assumptions for two-person games, stops here and there to admire a particularly interesting specimen, and the moves on. This is a delightful approach for both the casual reader, who is not interested in complex details, and the professional student of game theory, who is tired of taking a highly specific game and absolutely beating it to death with forays of analytical purity.One serious limitation of this book is that Skyrms is almost single-mindedly concerned with two-player games, whereas understanding human social life requires n-player games for fairly high n (at least 20 in some important cases). While a deep understanding of two-person games does shed light on behavior in larger games, it also can be very misleading. Certainly human society is much more complicated than one might infer from the workings of the prisoner's dilemma, the stag hunt, and the hawk-dove game.I also believe that Skyrms' major point in this book is just dead wrong. In the Preface, Skyrms says "If one simple game is to be chosen as an exemplar of the central problem of the social contract, which should it be? Many modern thinkers have focused on the prisoner's dilemma, but I believe that this emphasis is misplaced. The most appropriate choice is not the prisoner's dilemma, but rather the stag hunt." (p. xii) Now, the stag hunt is a pure coordination game of the following form. Suppose there are n players (Skyrms prefers two players, but any n will do). If all players "hunt stag," each will receive an payoff of 1000 calories of meat. However, if any player decides instead to "hunt rabbit," the stag hunt will fail, and all players will get no calories except the rabbit hunter, who gets 100 calories. This is a coordination game, or an assurance game, because a player can be assured of getting 100 calories no matter what the others do (by hunting rabbit), but if the players can coordinate so all hunt stag, they will all do much better.Skyrms defends his statement that human social life is basically a stag hunt-like coordination game as follows. At first sight, social cooperation seems to be a prisoner's dilemma, or in the n-player case, a public goods game. In this game, by cooperating an individual helps all the other members of the group, but at a cost to himself. Therefore, a self-regarding player will never cooperate. It follows that social cooperation requires altruistic players---people must cooperate even though this is personally costly and the others alone benefit from one's prosocial behavior. It is easy to see why the public goods game is an allegory for social cooperation among humans. For instance, if we all hunt, if hunting is dangerous and exhausting, and we must share the kill equally, then a self-regarding hunter will prefer to shirk rather than hunt. Cooperation in this case requires altruistic hunters. Skyrms' point, however, is that if the game is repeated indefinitely, then cooperation among self-regarding agents is possible using what are known as "trigger strategies." A trigger strategy for a player is to cooperate on every round, as long as all other players cooperate as well. However, the first time one player defects, the trigger strategy dictates that all players defect on every succeeding round. It is easy to see that in this case, even selfish players will cooperate on all rounds, because the gains they have from defecting on one rounds may be swamped by the losses incurred by not benefiting from others' efforts on the succeeding rounds.Why is Skyrms wrong? Note first that the repeated prisoner's dilemma or n-player public goods game (the latter is just a prisoner's dilemma with n players) is not really a stag hunt game at all. The stag hunt game has exactly two equilibria, one where everyone hunts rabbit and one where everyone hunts stag. The repeated public goods game (rppg) has an infinite number of equilibria! For instance, suppose it costs 100 calories to generate 1000 calories for the other players. Now suppose in a ten player repeated public goods game, all players cooperate on all rounds, except player 1, who defects on all rounds. With an obvious alteration in the trigger strategies of players 2 through n, we still have a Nash equilibrium of the rppg. This is because 9,000 calories are generated in each period, so each player gets 900 calories, and players 2 through 10 only expend 100 calories, so they have a net gain of 800 calories and hence are willing to participate. Now, by varying who participates and how much, we can generate an infinite number of equilibria for the rppg. In game theory, this is known as the Folk Theorem of Repeated Games.Despite the fact that the stag hunt is not exactly the same as the rppg, Skyrms would be correct in principle if it were true that the rppg were a coordination game, like the stag hunt. But the rppg is NOT a coordination game at all! In fact, in the rppg, a self-regarding player has an incentive to shirk if he can get away with it; i.e., if others do not observe his shirking. This is not the case in the stag hunt. Economists generally treat the Folk Theorem as a brilliant solution to the problem of cooperation among many self-regarding agents, and Skyrms is here merely following their lead. My study of the Folk Theorem, by contrast, shows that the Folk Theorem is no solution at all, except for groups of size two, or larger groups under generally implausible informational conditions (see my book, The Bounds of Reason, Princeton University Press, 2009). The reasons is that cooperation in the rppg requires that each player send a very accurate signal to each other player indicating cooperation or defection, and the same signal must be transmitted to all players if they are to coordinate in their manner of reacting to a defection. When different players get different signals (e.g., when each player sees only a subset of the other players) and/or when the signals have a significant probability of being inaccurate (e.g., a hunter worked hard but by chance failed to be successful in the hunt), the cooperative equilibrium to the rppg will not exist, or will exist but will be extremely inefficient.The implication of Skyrms' position for social theory is quite dramatic. If he were correct, it would follow that humans could cooperate very effectively even if they were perfectly self-regarding, with absolutely no need for altruistic preferences, empathy, no predisposition for cooperating and sharing, nor any other prosocial behavior that goes beyond simple mutualism: An individual would help the group only as a byproduct of helping himself. In fact, there is a great deal of evidence that humans have fundamental other-regarding preferences, including a predisposition to follow legitimate social norms, and to make personal sacrifices on behalf of the group if they perceive that others are make such sacrifices as well. My reading of the empirical evidence is that humans have evolved a social psychology that lead them to cooperate with others even when there is a personal cost, so long as others are doing the same. This implies that to sustain cooperation in a social group, we need a lot more than to simply coordinate on the high-yield strategy. We need a social system that fosters a sense of morality that includes caring about others and sacrificing on behalf of society. When that morality is absent or in disrepair, life will be "poore, nasty, brutish, and short," to use Hobbes' famous words.

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