Game-theoretic analyses of coalition behavior

Abstract

Coalitions are frequently more visible than payoffs. The theory of n-person games seeks primarily to identify stable allocations of valued resources; consequently, it gives inadequate attention to predicting which coalitions form. This paper explores a way of correcting this deficiency of game-theoretic reasoning by extending the theory of two-person cooperative games to predict both coalitions and payoffs in a three-person ‘game of status’ in which each player seeks to maximize the rank of his total score.¹ To accomplish this, we analyze the negotiations within each potential two-person coalition from the perspective of Nash's procedure for arbitrating two-person bargaining games,² then assume that players expect to achieve the arbitrated outcome selected by this procedure and use these expectations to predict achieved ranks and to identify players' preferences between alternative coalition partners in order to predict the probability that each coalition forms.³ We test these payoff and coalition predictions with data from three laboratory studies, and compare the results with those attained in the same data by von Neumann and Morgenstern's solution of two-person cooperative games,⁴ Aumann and Maschler's bargaining set solution for cooperative n-person games,⁵ and an alternative model of coalition behavior in three-person sequential games of status.⁶