In one classic version of the game, each player is given an endowment, which they can keep or contribute to a common fund. The fund is multiplied and distributed equally to the players. This is a social environment that rewards defection, since players that don’t contribute get the highest returns. When actual people play the game, most start off moderately generous, but as soon as they realize that they are being exploited by others, they withhold their own contributions. Cooperation goes down the drain, leaving only defection and the lack of social benefits. There is no way to punish defectors in this version of the game, so the punish vs. ignore option is inoperative. The only way to punish defectors is to withhold one’s own cooperation; that is, to become a defector oneself.
The punishment option can be added to the game by allowing players to contribute to the first common fund, where it is multiplied and distributed as before, or to a second fund, where it is multiplied and used to punish defectors by deducting from their payoffs. When this version of the game is played by real people, if enough players are motivated to punish defectors, then cooperators earn the highest payoffs and everyone ends up cooperating. But there are still financial losers in this game and they are the punishers. Since they must pay to punish, they place themselves at a disadvantage compared to cooperators who don’t punish. The problem of free-riding hasn’t gone away, but merely relocated from the provision of the public good to its protection.
A lot depends on the multiplier of the punishment fund. If it is high, then a little goes a long way toward punishing defectors. If it is low, then punishment can only be levied at a substantial personal cost. A lot also depends on the number of members playing the game who are willing to punish. If they are many, then the per capita cost of punishment becomes low. If they are few, then the per capita cost becomes prohibitive. Acting like the Lone Ranger can get you killed.Now think of Donald Trump as the elected punisher.
Fighting Wall Street Predators with Game Theory
David Sloan Wilson | SUNY Distinguished Professor of Biology and Anthropology at Binghamton University and Arne Næss Chair in Global Justice and the Environment at the University of Oslo