Implementing egalitarianism in a class of Nash demand games
Emin Karagözoğlu () and
Shiran Rachmilevitch ()
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Shiran Rachmilevitch: University of Haifa
Theory and Decision, 2018, vol. 85, issue 3, No 12, 495-508
Abstract We add a stage to Nash’s demand game by allowing the greedier player to revise his demand if the demands are not jointly feasible. If he decides to stick to his initial demand, then the game ends and no one receives anything. If he decides to revise it down to $$1-x$$ 1 - x , where x is his initial demand, the revised demand is implemented with certainty. The implementation probability changes linearly between these two extreme cases. We derive a condition on the feasible set under which the two-stage game has a unique subgame perfect equilibrium. In this equilibrium, there is first-stage agreement on the egalitarian demands. We also study two n-player versions of the game. In either version, if the underlying bargaining problem is “divide-the-dollar,” then equal division is sustainable in a subgame perfect equilibrium if and only if the number of players is at most four.
Keywords: Nash demand game; Divide-the-dollar; Fair division (search for similar items in EconPapers)
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