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 sixteen games were four repetitions each of four game types, arranged in a 2 x 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 M (i)1 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.
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References
Albers, W.: Bloc forming tendencies as characteristics of the bargaining behavior in different versions of apex games. Beiträge zür experimentellen Wirtschaftsforschung. Ed. by H. Sauermann. Vol. VIL Tübingen 1978.
Aumann, R. J., and M. Maschler: The bargaining set for cooperative games. Advances in game theory. Ed. by M. Dresher, L. S. Shapley and A. W. Tucker. Princeton 1964.
Davis, M.: Game theory: A nontechnical introduction. New York 1970.
Davis, M., and M. Maschler: The kernel of a cooperative game. Naval Research Logistics Quarterly 12, 1965, 223–259.
Funk, S. G.: Value power and positional power in n-person games. L.L. Thurstone Psychometric Laboratory Report No. 152, Chapel Hill, 1970.
Horowitz, A. D.: A test of the core, bargaining set, kernel, and Shapley models in n-person quota games with one weak player. Theory and decision 8, 1977, 49–65.
Horowitz, A. D., and Am. Rapoport: Test of the kernel and two bargaining set models in four- and five-person games. Game theory as a theory of conflict resolution. Ed. by An. Rapoport. Dordrecht, 1974.
Kahan, J. P., and R. A. Helwig: Coalitions: A system of programs for computer-controlled bargaining games. General Systems 16, 1971, 31–41.
Kahan, J. P., and Am. Rapoport: Test of the bargaining set and kernel models in three-person games. Game theory as a theory of conflict resolution. Ed. by An. Rapoport. Dordrecht, 1974.
Kahan, J. P., and Am. Rapoport: When you don’t need to join: The effects of guaranteed payoffs on bargaining in three person cooperative games. Theory and Decision 8, 1977, 97–126.
Kahan, J. P., and Am. Rapoport: The influence of structural relationships on bargaining in 4-person apex games. European Journal of Social Psychology 9, 1979, 339–361.
Levinsohn, J. R., and Am. Rapoport: Coalition formation in multistage three-person cooperative games. Beiträge zur experimentellen Wirtschaftsforschung. Ed. by H. Sauermann. Vol. VII, Tübingen 1978.
Luce, R. D., and H. Raiffa: Games and decisions: Introduction and critical survey. New York 1957.
Maschler, M.: The power of a coalition. Management Science 10, 1963a, 8–29.
Maschler, M.: n-Person games with only 1, n - 1, and n-person permissible coalitions. Journal of Mathematical Analysis and Applications, 6, 1963b, 230–256.
Maschler, M.: Playing an n-person game: An experiment. Princeton: Economic Research Program, Research Memorandum No. 73, Princeton 1965.
Maschler, M.: Playing an N-person game: An experiment. Beiträge zur experimentellen Wirtschaftsforschung. Ed. by H. Sauermann. Vol. VII, Tübingen 1978.
Medlin, S. M.: Effects on grand coalition payoffs on coalition formation in 3-person games. Behavioral Science 21, 1976, 48–61.
Michener, H. A., M. M. Sakurai, K. Yuen, and T. J. Kasen: A competitive test of the M1 (i) and M1 (im)bargaining set solutions in three-person conflicts. Journal of Conflict Resolution 23, 1979, 102–119.
Michener, H. A. K. Yuen, and I. J. Ginsberg: A competitive test of the M1 (im) bargaining set, kernel, and equal share models. Behavioral Science 22, 1977, 341–355.
Murnighan, J. K, and A. E. Roth: The effects of communication and information availability in an experimental study of a three-person game. Management Science 23, 1977, 1336–1348.
Owen, G.: Game theory. Philadelphia, 1968.
Peleg. B.: Existence theorem for the bargaining set M 1 (i). Essays in mathematical economics in honor of Oskar Morgenstern. Princeton, 1967.
Rapoport, Am., and J. P. Kahan: Computer controlled research on bargaining and coalition formation. Behavior Research Methods and Instrumentation 6, 1974, 87–93.
Rapoport, Am., and J. P. Kahan: When three isn’t always two against one: Coalitions in experimental three-person games. Journal of Experimental Social Psychology 12, 1976, 253–273.
Rapoport, Am., J. P. Kahan, and T. S. Wallsten: Sources of power in 4-person apex games. Beiträge zur experimentellen Wirtschaftsforschung. Ed. by H. Sauermann. Vol. VIII. Tübingen, 1978.
Rapoport, An.: n-person game theory: Concepts and applications. Ann Arbor, Michigan, 1970.
Riker, W. H.: Bargaining in a three-person game. American Political Science Review 61, 1967, 642–656.
Riker, W. H.: Three-person coalitions in three-person games: Experimental verification of the theory of games. Mathematical Applications in Political Science VI. Ed. by J. F. Herndon and J. L. Bernd. Charlottesville 1972.
Riker, W. H., and W. J. Zavoina: Rational behavior in politics: Evidence from a three-person game. American Political Science Review 64, 1970, 48–60.
Schelling, T. C: The strategy of conflict. Cambridge, 1960.
Selten, R., and K. G. Schuster: Psychological variables and coalition forming behavior. Risk and Uncertainty.. Ed. by K. Borch and D. Mossin. London, 1968.
von Neumann J., and O. Morgenstern: Theory of games and economic behavior, 2nd. ed. Princeton, N.J., 1947.
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© 1990 Kluwer Academic Publishers
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Rapoport, A. (1990). Standards of Fairness in 4-Person Monopolistic Cooperative Games. In: Experimental Studies of Interactive Decisions. Theory and Decision Library, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1992-1_10
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DOI: https://doi.org/10.1007/978-94-009-1992-1_10
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