By E. Roy Weintraub
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Extra info for Conflict and Co-operation in Economics
In fact, the social payoffs would be (if utilities could be added, which they cannot be) ranked in descending order as (- 2, - 2), (-10, -10), (- 20, -1), which equals (-1,-20), or -4,-20,-21. If the two prisoners thought as one, or if an impartial referee (lawyer) were to give binding counsel to the prisoners, the (As,Bs) strategy of mutual non-confession would certainly be chosen, and would, too, qualify as an equilibrium outcome. In short, the strategy pair (AT,B T) is 'rational' for the individuals qua individuals, while the pair (AN,BN) is 'rational' for the group of individuals.
That is, although the players cannot communicate directly, they can 37 'signal' their willingness to co-operate with each other by playing co-operative strategies in initial trial runs of the game in order to establish their intentions. If such a strategy is met with selection of the co-operative strategy by the opponent, each will continue to achieve the 'group rational' outcome. If 'nonconfession' is met by 'confession', however, the initial trust is replaced with non-co-operation and both players are thereby punished.
Of fish to get xOR of wheat, Frz also has moved to his strictly better set from Xl. Since the trade is viable, it is clear that this suggested trade dominates Xl (although there is no reason to suppose that it itself is undominated). In short, if any candidate for the title 'equilibrium trade' exists, it must be undominated. For just two traders, the undominated trades were coextensive with the contract curve defined by equal marginal rates of substitution. For two traders of each type, the set of undominated trades is smaller, and is in fact a proper subset of the original contract curve.