Incentivizing Cooperation in Noncooperative Games I: Simple Transfers in Games of Income

Consider a noncooperative game at whose outcomes commodities accrue to players, which are both valued by them and susceptible to transfer between them. In this situation, outcome-contingent transfers of commodities form a natural schema for incentivizing cooperation, potentially leading to Nash Equilibria (NE) that are better for all players. However, as in the folk theorem for repeated games, an embarrassingly large set of NE may be sustainable via transfers. The main source for this pathology is the possibility of a "threat", which can be understood as an "off-shell" transfer, i.e. a transfer that is contracted to take place at an outcome that is not actually being reached with positive probability at the strategy selection under consideration. Our goal is to restore the discriminatory nature of NE by means of a simple idea. We call an NE of the post-transfers game transparent if there are no off-shell transfers. This can also be viewed via the lens of "credibility", of something being seen in order to be believed. Among the transparent equilibria it is natural to focus on those that Pareto-improve players’ payoffs as much as possible with respect to a status quo NE of the pre-transfer game. In addition, if a social welfare function is specified, then one may ask for points in the Pareto-set that maximize welfare and achieve the gains to transfer. By way of illustration we analyze three classical non-cooperative games. These are the Centipede Game, Contest, and the Prisoners’ Dilemma; the last of which we discuss in some detail.