This article defines two new solution concepts for non-sidepayment games - the λ-transfer nucleolus and the λ-transfer disruption value - and reports the results of an experiment testing their predictive accuracy against that of a third solution concept, the well-known λ-transfer value (Shapley, 1969). The test was based on data from a laboratory experiment utilizing five-person, two-choice games that were constant-sum in normal form. Goodness-of-fit results show that the λ-transfer value and the λ-transfer disruption value were about equally accurate in predicting the observed payoffs to players in these games; both of these solutions were more accurate than the λ-transfer nucleolus.
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References
1.
Aumann, R. J. (1961) “The core of a cooperative game without sidepayments.”Transactions of the Amer. Mathematical Society98: 539-552.
2.
Aumann, R. J. (1985) “An axiomatization of the non-transferable utility value.”Econometrica 53: 599-612.
3.
Bonacich, P. (1979) “A single measure for point and interval predictions of coalition theories.”Behavioral Science24: 85-93.
4.
Champsaur, P. (1975) “Cooperation versus competition.”J. of Econ. Theory11: 394-417.
5.
Charnes, A. , J. Rousseau, and L. Seiford (1978) “Complements, mollifiers and the propensity to disrupt.”Int. J. of Game Theory7: 37-50.
6.
Gately, D. (1974) “Sharing the gains from regional cooperation: a game theoretic application to planning investment in electric power.”Int. Econ. Rev.15: 195-208.
7.
Harsanyi, J. C. (1963) “A simplified bargaining model for the n-person cooperative game.”Int. Econ. Rev.4: 194-220.
8.
Kahan, J. P. and A. Rapoport (1984) Theories of Coalition Formation. Hillsdale, NJ: Lawrence Erlbaum.
9.
Kirk, R. E. (1982) Experimental Design: Procedures for the Behavioral Sciences. (2nd ed.). Monterey, CA: Brooks/Cole.
10.
Kohlberg, E. (1971) “On the nucleolus of a characteristic function game.”Siam J. of Applied Mathematics20: 62-66.
11.
Komorita, S. S. (1978) “Evaluating coalition theories: some indices.”J. of Conflict Resolution22: 691-706.
12.
Littlechild, S. C. and K. G. Vaidya (1976) “The propensity to disrupt and the disruption nucleolus of a characteristic function game.”Int. J. of Game Theory5: 151-161.
13.
Maschler, M. , B. Peleg, and L. S. Shapley (1979) “Geometric properties of the kernel, nucleolus, and related solution concepts.”Mathematics of Operations Research4: 303-338.
14.
Michener, H. A. , Y. C. Choi, and D. C. Dettman (1986) “Stability by deterrence in cooperative non-sidepayment n-person games.”J. of Econ. Behavior and Organization7: 375-402.
15.
Michener, H. A. , D. C. Dettman, and Y. C. Choi (1984) “The beta-core solution in cooperative non-sidepayment n-person games,” pp. 145-181 in E. J. Lawler (ed.) Advances in Group Processes, Vol. 1. Greenwich, CT: Jai.
16.
Michener, H. A. and K. Potter (1981) “Generalizability of tests in n-person sidepayment games.”J. of Conflict Resolution25: 733-749.
17.
Michener, H. A. , K. Potter, C. G. Depies, and G. B. Macheel (1984) “A test of the core solution in finite strategy non-sidepayment games.”Int. J. of Mathematical Social Sciences8: 141-168.
18.
Michener, H. A. , K. Potter, and M. M. Sakurai (1983) “On the predictive efficiency of the core solution in side-payment games.”Theory and Decision15: 11-28.
19.
Michener, H. A. , M. S. Salzer, and M. S. Reimer (1987) “A test of the lambda-transfer value and lambda-transfer nucleolus in constant-sum non-sidepayment games.” Technical Report, University of Wisconsin-Madison.
20.
Murnighan, J. K. (1978) “Models of coalition behavior: game theoretic, social psychological, and political perspectives.”Psych. Bull.85: 1130-1153.
21.
Owen, G. (1972) “Values of games without side payments.”Int. J. of Game Theory1: 95-109.
22.
Owen, G. (1982) Game Theory (2nd ed.). New York: Academic Press.
23.
Rapoport, A. and J. P. Kahan (1976) “When three is not always two against one: coalitions in experimental three-person cooperative games.”J. of Experimental Social Psychology12: 253-273.
24.
Roth, A. E. (1980) “Values for games without sidepayments: some difficulties with current concepts.”Econometrica48: 457-465.
25.
Scarf, H. E. (1967) “The core of an n-person game.”Econometrica35: 50-69.
26.
Schmeidler, D. (1969) “The nucleolus of a characteristic function game.”Siam J. of Applied Mathematics17: 1163-1170.
27.
Shapley, L. S. (1953) “A value for n-person games,” in A. W. Kuhn and A. W. Tucker (eds.) Contributions to the Theory of Games, Vol. 2. Princeton, NJ: Princeton Univ. Press.
28.
Shapley, L. S. (1969) “Utility comparison and the theory of games,” in G. T. Guilbaud (ed.) La Decision. Paris: Editions de Centre National de la Recherche Scientifique.
29.
Shapley, L. S. and M. Shubik (1969) “Pure competition, coalition power, and fair division.”Int. Econ. Rev.3: 337-362.
30.
Von Neumann, J. and O. Morgenstern (1953) Theory of Games and Economic Behavior (3rd ed.). Princeton, NJ: Princeton Univ. Press.
