# zbMATH — the first resource for mathematics

Predictive superiority of the beta-characteristic function in cooperative non-sidepayment n-person games. (English) Zbl 0605.90142
This article reports an experimental study of decision-making outcomes in cooperative non-sidepayment games. The objective of this test was to determine which characteristic function, $$V_{\alpha}(S)$$ or $$V_{\beta}(S)$$, provides the most accurate basis for payoff predictions from solution concepts. The experiment tested three solution concepts (core, stable set, imputation set) in the context of 5-person, 2-strategy non-sidepayment games. Predictions from each of the three solution concepts were computed on the basis of both $$V_{\alpha}(S)$$ and $$V_{\beta}(S)$$, making a total of six predictive theories under test. Consistent with earlier studies [H. A. Michener, D. C. Dettman and Y. C. Choi, in: Advances in Group Processes 1, JAI Press, Greenwich, CT (1984); H. A. Michener, D. C. Dettman, J. M. Ekman and Y. C. Choi, ”A comparison of the alpha- and beta characteristic functions in cooperative non-sidepayment n-person games”, Techn. Report, Dept. of Sociology, Univ. of Wisconsin at Madison (1985)], two basic findings emerged. First, the data show that for each of the solutions tested, the prediction from any solution concept computed from $$V_{\beta}(S)$$ was more accurate than the prediction from the same solution concept computed from $$V_{\alpha}(S)$$. Second, the $$\beta$$- core was the most accurate of the six theories tested. Overall, these results support the view that $$V_{\beta}(S)$$ is superior to $$V_{\alpha}(S)$$ as a basis for payoff predictions in cooperative non- sidepayment games.
##### MSC:
 91A12 Cooperative games 91D99 Mathematical sociology (including anthropology) 91E99 Mathematical psychology
Full Text:
##### References:
 [1] Aumann, R. J.: 1961, ?The Core of a Cooperative Game Without Sidepayments?, Transactions of the American Mathematical Society 98, 539-552. · Zbl 0099.36602 · doi:10.1090/S0002-9947-1961-0127437-2 [2] Aumann, R. J.: 1967, ?A Survey of Cooperative Games Without Side Payments?, in M. Shubik (ed.), Essays in Mathematical Economics, Princeton University Press, Princeton, NJ. [3] Aumann, R. J. and Peleg, B.: 1960, ?von Neumann-Morgenstern Solutions to Cooperative Games Without Side Payments?, Bulletin of the American Mathematical Society 66, 173-179. · Zbl 0096.14706 · doi:10.1090/S0002-9904-1960-10418-1 [4] Gillies, D. B.: 1959, ?Solutions to General Non-zero-sum Games?, Annals of Mathematics Studies 40, 47-85. · Zbl 0085.13106 [5] Hart, S. and Kurz, M.: 1983, ?Endogenous Formation of Coalitions?, Econometrica 51, 1047-1064. · Zbl 0523.90097 · doi:10.2307/1912051 [6] Jentzsch, G.: 1964, ?Some Thoughts on the Theory of Cooperative Games?, Annals of Mathematics Studies 52, 407-442. · Zbl 0127.37303 [7] Kirk, R. E.: 1968, Experimental Design: Procedures for the Behavioral Sciences, Brooks/Cole, Belmont, CA. · Zbl 0414.62054 [8] Komorita, S. S.: 1978, ?Evaluating Coalition Theories: Some Indices?, Journal of Conflict Resolution 22, 691-706. · doi:10.1177/002200277802200407 [9] Michener, H. A. and Potter, K.: 1981, ?Generalizability of Tests in n-Person Sidepayment Games?, Journal of Conflict Resolution 25, 733-749. [10] Michener, H. A. Dettman, D. C., and Choi, Y. C.: 1984a, ?The Beta-core Solution in Cooperative Non-sidepayment n-Person Games?, in E. J. Lawler (ed.), Advances in Group Processes 1, JAI Press, Greenwich, CT. · Zbl 0567.90100 [11] Michener, H. A., Potter, K., Macheel, G. B., and Depies, C. G.: 1984b, ?A Test of the von Neumann-Morgenstern Stable Set Solution in Cooperative Non-sidepayment n-Person Games?, Behavioral Science 29, 13-27. · Zbl 0552.90103 · doi:10.1002/bs.3830290103 [12] Michener, H. A., Potter, K., Depies, C. G., and Machael, G. B.: 1984c, ?A Test of the Core Solution in Finite Strategy Non-sidepayment Games?, International Journal of Mathematical Social Sciences, 8, 141-168. · Zbl 0552.90103 · doi:10.1016/0165-4896(84)90012-X [13] Michener, H. A., Dettman, D. C., Ekman, J. M., and Choi, Y. C.: 1985, ?A Comparison of the Alpha- and Betacharacteristic Functions in Cooperative Non-sidepayment n-Person Games?, Technical Report, Dept. of Sociology, University of Wisconsin-Madison. · Zbl 0567.90100 [14] Owen, G.: 1982, Game Theory, 2nd edition, Academic Press, New York. · Zbl 0544.90103 [15] Peleg, B.: 1963, ?Bargaining Sets of Cooperative Games Without Side Payments?, Israel Journal of Mathematics 1, 197-200. · Zbl 0212.25102 · doi:10.1007/BF02759717 [16] Rapoport, A. and Kahan, J. P.: 1976, ?When Three Is Not Always Two Against One: Coalitions in Experimental Three-person Cooperative Games?, Journal of Experimental Social Psychology 12, 253-273. · doi:10.1016/0022-1031(76)90056-1 [17] Rosenthal, R. W.: 1972, ?Cooperative Games in Effectiveness Form?, Journal of Economic Theory 5, 88-101. · doi:10.1016/0022-0531(72)90120-2 [18] Scarf, H. E.: 1967, ?The Core of an n-Person Game?, Econometrica 35, 50-69. · Zbl 0183.24003 · doi:10.2307/1909383 [19] Scarf, H. E.: 1971, ?On the Existence of a Cooperative Solution for a General Class of n-Person Games?, Journal of Economic Theory 3, 169-181. · doi:10.1016/0022-0531(71)90014-7 [20] Shubik, M.: 1971, ?Games of Status?, Behavioral Science 16, 117-129. · doi:10.1002/bs.3830160202 [21] Shubik, M.: 1982, Game Theory in the Social Sciences, MIT Press, Cambridge, MA. · Zbl 0903.90179 [22] von Neumann, J. and Morgenstern, O.: 1944, The Theory of Games and Economic Behavior, Princeton University Press, Princeton, NJ (third edn., 1953). · Zbl 0063.05930
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.