Achieving Efficiency with Manipulative Bargainers∗

Abstract: Two agents bargain over the allocation of a bundle of divisible com-modities. After strategically reporting utility functions to a neutral arbitrator, the outcome is decided by using a bargaining solution concept chosen from a fam-ily that includes the Nash and the Raiffa-Kalai-Smorodinsky solutions. When reports are restricted to be continuous, strictly increasing and concave, it has been shown that this kind of “distortion game ” leads to inefficient outcomes. We study the distortion game originated when agents are also allowed to claim non-concave utility functions. Contrasting with the previous literature, any interior equilibrium outcome is efficient and any efficient allocation can be supported as an equilibrium outcome of the distortion game. In a similar fashion to the Nash demand game we consider some uncertainty about the opponent’s features to virtually implement the Nash bargaining solution. Key words: bargaining, distortion games, efficiency.