prisca theologica See FICINO. prisoner’s dilemma, a problem in game theory, and more broadly the theory of rational choice, that takes its name from a familiar sort of pleabargaining situation: Two prisoners (Robin and Carol) are interrogated separately and offered the same deal: If one of them confesses (‘defects’) and the other does not, the defector will be given immunity from prosecution and the other will get a stiff prison sentence. If both confess, both will get moderate prison terms. If both remain silent (cooperate with each other), both will get light prison terms for a lesser offense. There are thus four possible outcomes: (1) Robin confesses and gets immunity, while Carol is silent and gets a stiff sentence. (2) Both are silent and get light sentences. (3) Both confess and get moderate sentences. (4) Robin is silent and gets a stiff sentence, while Carol confesses and gets immunity. Assume that for Robin, (1) would be the best outcome, followed by (2), (3), and (4), in that order. Assume that for Carol, the best outcome is (4), followed by (2), (3), and (1). Each prisoner then reasons as follows: ‘My confederate will either confess or remain silent. If she confesses, I must do likewise, in order to avoid the ‘sucker’s payoff’ (immunity for her, a stiff sentence for me). If she remains silent, then I must confess in order to get immunity – the best outcome for me. Thus, no matter what my confederate does, I must confess.’ Under those conditions, both will confess, effectively preventing each other from achieving anything better than the option they both rank as only third-best, even though they agree that option (2) is second-best. This illustrative story (attributed to A. W. Tucker) must not be allowed to obscure the fact that many sorts of social interactions have the same structure. In general, whenever any two parties must make simultaneous or independent choices over a range of options that has the ordinal payoff structure described in the plea bargaining story, they are in a prisoner’s dilemma. Diplomats, negotiators, buyers, and sellers regularly find themselves in such situations. They are called iterated prisoner’s dilemmas if the same parties repeatedly face the same choices with each other. Moreover, there are analogous problems of cooperation and conflict at the level of manyperson interactions: so-called n-person prisoner’s diemmas or free rider problems. The provision of public goods provides an example. Suppose there is a public good, such as clean air, national defense, or public radio, which we all want. Suppose that is can be provided only by collective action, at some cost to each of the contributors, but that we do not have to have a contribution from everyone in order to get it. Assume that we all prefer having the good to not having it, and that the best outcome for each of us would be to have it without cost to ourselves. So each of us reasons as follows: ‘Other people will either contribute enough to produce the good by themselves, or they will not. If they do, then I can have it cost-free (the best option for me) and thus I should not contribute. But if others do not contribute enough to produce the good by themselves, and if the probability is very low that my costly contribution would make the difference between success and failure, once again I should not contribute.’ Obviously, if we all reason in this way, we will not get the public good we want. Such problems of collective action have been noticed by philosophers since Plato. Their current nomenclature, rigorous game-theoretic formulation, empirical study, and systematic philosophical development, however, has occurred since 1950.
See also GAME THEORY, SOCIAL CHOICE THEOR. L.C.B.