Remarks on Bargaining and Cooperation in Strategic Form Games

Zhigang Cao

Although possessing many beautiful features, the Hart and Mas-Colell bargaining model is not flawless: the concept of threat in this model may behave quite counter-intuitive, and its SP equilibrium expected payoff vector may not be the same as the min-max solution payoff vector in zero-sum games. If we postpone realizations of all threats to the end of the game, the two problems can be solved simultaneously. This is exactly the 2(a) model suggested by Hart and Mas-Colell in the last section of their paper. I show that the new model, unfortunately, can only guarantee the existence of an SP equilibrium in the two player case. For the original model, I reduce the computation of an SP equilibrium to a system of linear inequalities. Quantitative efficiency and symmetric SP equilibria are also discussed.

January, 2011
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