Title: Bargaining in strategic games with private information

Abstract:

There is an inherent tension between cooperation and competition in strategic games: act cooperatively to increase the size of the collective pie, and act selfishly to increase your share of it. We first survey early work on bargaining in strategic games with side payments, showing that a single "coco" solution coincides with many central concepts. For zero-sum games, the coco solution coincides with the von-Neumann minmax value. For TU variable-threat bargaining, it coincides with the Nash (1953), Raiffa (1953), Kalai-Smorodinsky (1975), and egalitarian solutions. The cooperation-competition tension only increases in the presence of private information. We attempt to resolve this tension via the coco solution for two-person private-information strategic games with side payments. Following Selten (1960), we justify the coco value by axioms of monotonicity and efficiency, imposed directly on the class of Bayesian strategic games. Finally, we introduce a simple incentive-compatible efficient mechanism that implements the coco solution in a broad class of games.