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. Martin Shubik, ‘Games of Status’, (1971), 117–129. 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, R. Duncan Luce and Howard Raiffa, , John Wiley and Sons, New York, 1958, pp. 121–143. 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. This work is supported by Research Grant SOC72-05245, awarded to the second author by the National Science Foundation. An earlier version of this paper was presented at the annual meetings of the American Political Science Association, Chicago, Ill., August 29 – September 2, 1974. We thank Peter C. Ordeshook for suggesting that Nash's arbitration model might be applied to this game, and David Deutsch for assisting us in this research. 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, Luce and Raiffa, , pp. 115–119. Aumann and Maschler's bargaining set solution for cooperative n-person games, R. J. Aumann and Michael Maschler, ‘The Bargaining Set for Cooperative Games’, in M. Dresher, L. S. Shapley, and A. W. Tucker (eds.), , Annals Math. Studies, No. 52, Princeton University Press, Princeton, New Jersey, 1964, pp. 443–476. and an alternative model of coalition behavior in three-person sequential games of status. For an extension and application of the bargaining set to three-person games of status and a comparison of the bargaining set with our alternative model of coalition behavior in the three laboratory studies reported in this paper, see Richard J. Morrison's Ph.D. thesis, ‘Rational Choice Models of Coalition Formation in the Triad’, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pennsylvania, 1974 (this dissertation is available from University Microfilms, Ann Arbor, Michigan); and the paper by Laing and Morrison, ‘Sequential Games of Status’, (1974), 177–197. The coalition model is developed more extensively by Laning and Morrison in “Coalitions and Payoffs in Three-Person Sequential Games: Initial Tests of Two Formal Models”, (1973), 3–26 (hereinafter cited as ‘Initial Tests of Two Formal Models’).