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A Risk-Dominant Allocation: Maximizing Coalition Stability

Authors


  • Matthew McGinty, University of Wisconsin-Milwaukee (mmcginty@umw.edu).

  • This paper has greatly benefited from the comments of an anonymous Associate Editor and referees, Dan Friedman, John Heywood, Frans de Vries, Scott Drewianka and a line of encouragement from Herve Moulin. All remaining errors are my own.

Abstract

This paper presents a rule to allocate a coalition’s worth for superadditive games with positive externalities. The allocation rule awards each member their outside payoff, plus an equal share of the surplus. The resulting allocation maximizes coalition stability. Stable coalitions are Strong Nash equilibria since no subset of members has an incentive to leave. Similarly, no subset of non-members has an incentive to join a stable coalition if the game is concave in this region. The allocation is risk-dominant. All stable coalitions are robust to the maximum probability of 50% that players’ deviate from their individual best-responses. The paper compares the allocation to the Shapley value and the Nash bargaining solution, and illustrates why these traditional rules result in small coalitions when applied to issues such as international environmental agreements.

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