By John W. Pratt, Richard J. Zeckhauser
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Extra resources for Principals and agents : the structure of business
It is also often called the Prisoners’ Dilemma (rs’, not r’s) ; whether one looks at from the point of the individual or the group, the prisoners have a problem. • The Prisoner’s Dilemma is not always defined the same way. If we consider just ordinal payoﬀs, then the game in Table 10 is a Prisoner’s Dilemma if T (temptation) > R(revolt) > P (punishment) > S(Sucker), where the terms in parentheses are mnemonics. This is standard notation; see, for example, Rapoport, Guyer & Gordon (1976), p. 400.
All of its equilibria are pareto-eﬃcient, because no player gains without another player losing. It is often said that strategy profile x “pareto dominates” or “dominates” strategy profile y. Taken literally, this is meaningless, since strategies do not necessarily have any ordering at all– one could define Deny as being bigger than Conf ess, but that would be arbitrary. ” 22 Very few games have a dominant strategy equilibrium, but sometimes dominance can still be useful even when it does not resolve things quite so neatly as in the Prisoner’s Dilemma.
Introduces granola bars, at considerable marketing expense in educating the public, then Smallpig Ltd. can imitate profitably without ruining Bigpig’s sales completely. If Smallpig introduces them at the same expense, however, an imitating Bigpig would hog the market. 27 box, them, as is especially suitable here). Double arrows or dotted circles indicate weakly dominant payoﬀs. Any payoﬀ profile in which every payoﬀ is circled, or which has arrows pointing towards it from every direction, is a Nash equilibrium.