This article reports an experimental test that juxtaposes the von Neumann-Morgenstern characteristic function v(S) against the homomollifier function h(S) proposed by Charnes et al. (1978). The test was conducted in the context of 5-person cooperative sidepayment non-constant-sum games with nonempty core. Experimental results show that payoff predictions by various solution concepts (the Shapley value, the nucleolus, the 2-center) computed from the homomollifier are more accurate than predictions by the same solutions computed from the characteristic function. Supplementary analyses of data show that the payoff function x(S) is more closely approximated by the homomollifier h(S) than by the characteristic function v(S). These findings are interpreted as indicating that the homomollifier is more useful than the characteristic function for purposes of predicting payoffs in non-constant-sum games.
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References
1.
Charnes, A. , and S. C. Littlechild (1975) “On the formation of unions in n-person games.”J. of Econ. Theory10: 386-402.
2.
Charnes, A. , J. Rousseau, and L. Seiford (1978) “Complements, mollifiers, and the propensity to disrupt.”Int. J. of Game Theory7: 37-50.
3.
Charnes, A. , J. Rousseau, and L. Seiford (1982) “Mollifiers for games in normal form and the Harsanyi-Selten valuation function.”Int. J. of Game Theory11: 163-174.
4.
Greisinger, D. W. and J. W. Livingston, Jr. (1973) “Toward a model of interpersonal motivation in experimental games.”Behavioral Sci.18: 173-188.
5.
Harsanyi, J. C. (1959) “A bargaining model for the cooperative n-person game.”Annals of Mathematics Studies40: 325-355.
6.
Harsanyi, J. C. (1963) “A simplified bargaining model for the n-person cooperative game.”Int. Econ. Rev.4: 194-220.
7.
Horowitz, A. D. (1977) “A test of the core, bargaining set, kernel, and Shapley models in n-person quota games with one weak player.”Theory and Decision8: 49-65.
8.
Jones, A. J. (1980) Game Theory: Mathematical Models of Conflict. Chichester, England: Ellis Horwood.
9.
Kahan, J. P. and A. Rapoport (1977) “When you don't need to join: the effects of guaranteed payoffs on bargaining in three-person cooperative games.”Theory and Decision8: 97-126.
10.
Kirk, R. E. (1968) Experimental Design: Procedures for the Behavioral Sciences. Belmont, CA: Brooks/Cole.
11.
Kohlberg, E. (1971) “On the nucleolus of a characteristic function game.”SIAM J. of Applied Mathematics20: 62-66.
12.
Komorita, S. S. and D. A. Kravitz (1981) “Effects of prior experience on coalition bargaining.”J. of Personality and Social Psychology40: 675-686.
13.
Luce, R. D. and H. Raiffa (1957) Games and Decisions. New York: John Wiley.
14.
Maschler, M. (1963) “The power of a coalition,”Management Sci.10: 8-29.
15.
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.
16.
McClintock, C. G. (1972) “Social motivation—a set of propositions.”Behavioral Sci.17: 438-454.
17.
McKinsey, J.C.C. (1952) Introduction to the Theory of Games. New York: McGraw-Hill.
18.
Medlin, S. M. (1976) “Effects of grand coalition payoffs on coalition formation in three-person games.”Behavioral Sci.21: 48-61.
19.
Michener, H. A. , P. D. Clancy, and K. Yuen (1984) “Do outcomes of n-person sidepayment games fall in the core?” in M. J. Holler (ed.) Coalition and Collective Action. Wurzburg: Physica-Verlag.
20.
Michener, H. A. , I. J. Ginsberg, and K. Yuen (1979) “Effects of core properties in four-person games with side-payments.”Behavioral Sci.24: 263-280.
21.
Michener, H. A. and K. Potter (1981) “Generalizability of tests in n-person sidepayment games.”J. of Conflict Resolution25: 733-749.
22.
Michener, H. A. and K. Potter and M. M. Sakurai (1983) “On the predictive efficiency of the core solution in side-payment games.”Theory and Decision15: 11-28.
23.
Michener, H. A. , K. Yuen, and S. B. Geisheker (1980) “Nonsymmetry and core size in n-person sidepayment games.”J. of Conflict Resolution24: 495-523.
24.
Michener, H. A. , K. Yuen, and M. M. Sakurai (1981) “On the comparative accuracy of lexicographical solutions in cooperative games.”Int. J. of Game Theory10: 75-89.
25.
Murnighan, J. K. and A. E. Roth (1977) “Effects of communication and information availability in an experimental study of a three-person game.”Management Sci.23: 1336-1348.
26.
Murnighan, J. K. and A. E. Roth (1978) “Large group bargaining in a characteristic function game.”J. of Conflict Resolution22: 299-317.
27.
Murnighan, J. K. and A. E. Roth (1980) “Effects of group size and communication availability on coalition bargaining in a veto game.”J. of Personality and Social Psychology39: 92-103.
28.
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.
29.
Rapoport, A. , and J. P. KahanS. G. Funk, and A. D. Horowitz (1979) Coalition Formation by Sophisticated Players. New York: Springer-Verlag.
30.
Rosenthal, R. W. (1972) “Cooperative games in effectiveness form.”J. of Econ. Theory5: 88-101.
31.
Sakurai, M. M. (1980) “A competitive test of the descriptive accuracy of the characteristic function, power function, and Shapley value based function.”Theory and Decision12: 259-278.
32.
Schmeidler, D. (1969) “The nucleolus of a characteristic function game.”SIAM J. of Applied Mathematics17: 1163-1170.
33.
Selten, R. (1964) “Valuation of n-person games.”Annals of Mathematics Studies52: 577-626.
34.
Selten, R. (1972) “Equal share analysis of characteristic function experiments,” in H. Sauermann (ed.) Contributions to Experimental Economics, Vol. 3. Tubingen: Mohr.
35.
Shapley, L. S. (1953) “A value for n-person games.”Annals of Mathematics Studies28: 307-317.
36.
Spinetto, R. D. (1971) “Solution concepts of n-person cooperative games as points in game space.”Technical Report No. 138, Department of Operations Research, Cornell University.
37.
Spinetto, R. D. (1974) “The geometry of solution concepts for n-person cooperative games.”Management Sci.20: 1292-1299.
38.
Von Neumann, J. and O. Morgenstern (1953) Theory of Games and Economic Behavior. New York: John Wiley. (Originally published in 1944)
