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A comparison of the alpha- and beta-characteristic functions in cooperative non-sidepayment $$n$$-person games. (English) Zbl 0567.90100
Summary: This article reports a test of theories of payoff allocation in n-person game-theoretic systems. An experimental study was conducted to test the relative predictive accuracy of three solution concepts (imputation set, stable set, core) in the context of 4-person, 2-strategy non-sidepayment games. Predictions from each of the three solution concepts were computed on the basis of both $$\alpha$$-effectiveness (von Neumann-Morgenstern) and $$\beta$$-effectiveness (Aumann), making a total of six predictive theories under test. Two important results emerged. First, the data show that the $$\beta$$-imputation set was more accurate than the $$\alpha$$-imputation set, the $$\beta$$-stable set was more accurate than the $$\alpha$$-stable set, and the $$\beta$$-core was more accurate than the $$\alpha$$-core; in other words, for each of the solutions tested, the prediction from any solution concept based on $$\beta$$-effectiveness was more accurate than the prediction from the same solution based on $$\alpha$$-effectiveness. Second, the $$\beta$$-core was the most accurate of the six theories tested. Results are interpreted as showing that $$\beta$$-effectiveness is superior to $$\alpha$$-effectiveness as a basis for payoff predictions in cooperative non-sidepayment games.

##### MSC:
 91A12 Cooperative games 91A90 Experimental studies 91E99 Mathematical psychology
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##### References:
 [1] Aumann R. J., Transactions of the American Mathematical Society 98 pp 539– (1961) · doi:10.1090/S0002-9947-1961-0127437-2 [2] Aumann R. J., Essays in Mathematical Economics. (1967) [3] Aumann R. J., Bulletin of the American Mathematical Society 66 pp 173– (1960) · Zbl 0096.14706 · doi:10.1090/S0002-9904-1960-10418-1 [4] Gillies D. B., Annals of Mathematics Studies 40 pp 47– (1959) [5] Jentzsch G., Annals of Mathematics Studies 52 pp 407– (1964) · Zbl 0127.37303 [6] Kirk R. E., Experimental Design: Procedures for the Behavioral Sciences. (1968) · Zbl 0414.62054 [7] Komorita S. S., Journal of Conflict Resolution 22 pp 691– (1978) · doi:10.1177/002200277802200407 [8] Michener H. A., Advances in Group Processes 1 (1984) [9] Michener H. A., Journal of Conflict Resolution 25 pp 733– (1981) [10] Michener H. A., Behavioral Science 29 pp 13– (1984) · doi:10.1002/bs.3830290103 [11] Michener H. A., International Journal of Mathematical Social Sciences 8 pp 141– (1984) · Zbl 0552.90103 · doi:10.1016/0165-4896(84)90012-X [12] Owen G., Game Theory,, 2. ed. (1982) [13] Peleg B., Israel Journal of Mathematics 1 pp 197– (1963) · Zbl 0212.25102 · doi:10.1007/BF02759717 [14] Rapoport A., Journal of Experimental Social Psychology 12 pp 253– (1976) · doi:10.1016/0022-1031(76)90056-1 [15] Scarf H. E., Econometrica 35 pp 50– (1967) · Zbl 0183.24003 · doi:10.2307/1909383 [16] Scarf H. E., Journal of Economic Theory 3 pp 169– (1971) · doi:10.1016/0022-0531(71)90014-7 [17] Shubik M., Behavioral Science 16 pp 117– (1971) · doi:10.1002/bs.3830160202 [18] Shubik M., Game Theory in the Social Sciences. (1982) · Zbl 0903.90179 [19] von Neumann J., The Theory of Games and Economic Behavior. (1944) · Zbl 0063.05930
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