Dominant Strategy Implementation of Bargaining Solutions

Hideki Mizukami
College of Economics, Aoyama Gakuin University

Takuma Wakayama
Ryukoku University

April 18, 2012

Abstract:

We consider problems where agents bargain over their shares of a divisible commodity. The purpose of this paper is to explore the relationship between dominant strategy implementability and the axioms of bargaining solutions. We first provide a complete characterization of dominant strategy implementable allocation rules. Next, we show that an allocation rule inducing a bargaining solution is dominant strategy implementable and satisfies a very mild condition called non-disagreement if and only if the bargaining solution satisfies efficiency, scale invariance, and strong monotonicity, provided that there are two agents. By incorporating the result of Roemer (1996), we can establish that in the two-agent case, only dictatorial solutions are induced by dominant strategy implementable allocation rules satisfying non-disagreement. Further, it turns out that if there are three or more agents, then the above three axioms of bargaining solutions are still sufficient but not necessary for a bargaining solution to be induced by a dominant strategy implementable allocation rule satisfying non-disagreement.

Dominant Strategy Implementation of Bargaining Solutions

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