Abstract
Six quartets of players participated in a sequence of 16 4-person nonconstant-sum characteristic function games in which one player (the monopolist) was necessarily a member of any coalition that could form. The 16 games were four repetitions each of four game types, arranged in a 2 × 2 design depending on (i) whether or not the grand coalition of all four players was allowed to form and (ii) whether or not the monopolist players were symmetric. The outcomes of these games were compared to predictions derived from the (math) bargaining set [Maschler, 1963b], and from a modification of Maschler’s [1963a] power model.
The results indicated that each quartet established a standard for the range of the monopolist’s payoff early in the sequence, and that this standard took on the function of a norm in defining the legitimate bargaining ground for that quartet for the remainder of the sequence. Two quartets’ standards were well within the prediction of the bargaining set; one quartet supported the power model. Analysis of the patterns of coalition structure and rudimentary analyses of the bargaining processes indicate that the central concept of standards of fairness underlying the power model is appropriate and timely.
Research reported in this paper was supported by National Science Foundation Grant BNS76-84285. This paper was written while both authors were Fellows-in-Residence at the Netherlands Institute for Advanced Study in the Humanities and Social Sciences. We wish to thank S.G. Funk and A.D. Horowitz for their assistance in data collection and analysis. We wish particularly to thank Michael Maschler, with whom we have had a long and lively interaction on the power model, for his many helpful comments and suggestions for improving the paper.
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Rapoport, A., Kahan, J.P. (1979). Standards of Fairness in 4-Person Monopolistic Cooperative Games. In: Brams, S.J., Schotter, A., Schwödiauer, G. (eds) Applied Game Theory. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-41501-6_5
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