Equilibrium Computation of the Hart and Mas-Colell Bargaining Model
Mathematical Social Sciences, 2013, 66:152-162
19 Pages Posted: 1 Apr 2013 Last revised: 27 Jul 2014
Date Written: March 24, 2013
The 8th problem raised by [Hart and Mas-Colell (2010) Bargaining and Cooperation in Strategic Form Games. Journal of the European Economics Association, 8(1): 7-33], is solved. To be specific, I show that the set of SP equilibria can be determined by a finite number of systems of linear inequalities, which are efficiently solvable when there are two players. This is more or less surprising because the Hart and Mas-Colell bargaining model and the SP equilibrium both seem to be rather complicated, and it is well known that an arbitrary Nash equilibrium is hard to compute, even when there are only two players. Using this algorithm, it is shown that players of Prisoners' Dilemma can cooperate to some extent in the Hart and Mas-Colell bargaining, and full cooperation is attainable as \rho, a parameter of this model, approaches to 1. Quantitative efficiency, i.e. price of anarchy, is also analyzed.
Keywords: game theory, bargaining, cooperation, equilibrium computation, complementary slackness
JEL Classification: C63, C78
Suggested Citation: Suggested Citation