This paper introduces some concepts of equilibrium payoff configurations for n-person games. They are based on the idea that a coalition must be sufficiently stable to break away from a particular payoff configuration and are extensions of the core and the bargaining sets The question of general existence is dealt with, as well as interesting dynamic properties in three-person games
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References
1.
Aumann, R.J. and J.H. Dreze (1974) "Cooperative games with coalition structures."Int. J. of Game Theory3: 217-237.
2.
Aumann, R.J. and M. Maschler (1964) "The bargaining sets for cooperative games," pp. 443-476 in M. Dresher et al. (eds.) Advances in Game Theory (Annals of Mathematical Studies, No. 52). Pnnceton, NJ: Princeton Univ. Press.
3.
Charnes, A. and S. Littlechild (1975) "On the formation of unions in n-persons
4.
Charnes, A. and S. Littlechild (1975) "On the formation of unions in n-person games."J. of Economic Theory10: 386-402.
5.
——— and S. Sorensen (1973) "Core-stem solutions of n-person essential games."Socio-Econ. Plan. Sci. 7: 649-660.
6.
Davis, M. and M. Maschler (1965) "The kernel of a cooperative game."Naval Research Logistics Q. 12: 223-259.
7.
Gillies, D.B. (1959) "Solutions to general non-zero-sum games," pp. 47-85 in R. D. Luce and A. W. Tucker (eds.) Contributions to the Theory of Games, Vol. 4 (Annals of Mathematical Studies, No. 40). Princeton, NJ: Pnnceton Univ. Press.
8.
Horowitz, A.D. (1973) "The competitive bargaining set for cooperative n-person games."J. of Math. Psychology10: 265-289.
9.
——— and A. Rapoport (1974) "Test of the kernel and two bargaining set models in four- and five-person games," pp. 161-192 in A. Rapoport (ed.) Game Theory as a Theory of Conflict Resolution. Dordrecht : D. Reidel.
10.
Kalisch, G.K., J.W. Milnor, J.F. Nash, and E.D. Nering (1954) "Some experimental n-person games," pp. 301-327 in R. M. Thrall et al. (eds.) Decision Processes. New York: John Wiley.
11.
Luce, R.D. and H. Raiffa (1957) Games and Decisions: Introduction and Critical Survey. New YorkJohn Wiley.
12.
Maschler, M. (1962) "An experiment on n-person games." Recent Advances of Game Theory, Princeton University Conference.
13.
Medlin, S.M. (1976) "Effects of grand coalition payoffs on coalition formation in three-person games."Behavioral Sci. 21: 48-61.
14.
Rapoport, A. (1970) N-person Game Theory: Concepts and Applications . Ann Arbor: Univ. of Michigan Press.
15.
Rosenthal, R.W. (1970) "Stability analysis of cooperative games in effectiveness form." Technical Reprot No. 70-11Stanford, CA: Stanford University. Department of Operations Research.
16.
Roth, A.E. (1974) "Subsolutions of cooperative games." Technical Report No. 118. Stanford CA: Stanford University. Institute for Mathematical Studies in the Social Sciences.
17.
Schmeidler, D. (1969) "The nucleolus of a characteristic function game."SIAM J. of Applied Math. 17. 1163-1170.
18.
Selten, R. and K.G. Schuster (1968) "Psychological variables and coalition-forming behavior," pp. 221-240 in K. Borch and J. Mossin (eds.) Risk and Uncertainty . London: Macmillan.
19.
Sussangkarn, C. (n.d.a) "Some stability concepts for n-person games." Doctoral dissertation , in progress.
20.
Vilkas, E. (1976) "On a general approach to optimality in game theory." Cowles Foundation Discussion Paper No. 419. New Haven, CT: Yale University.
21.
Von Neumann, J. and O. Morgenstern (1944) Theory of Games and Economic Behavior. Pnnceton, NJ: Princeton Univ. Press.
22.
Westen, T.E. and J.J. Buckley (1974) "Toward an explanation of experimentally obtained outcomes to a simple, majority rule game."J. of Conflict Resolution18: 198-236.
23.
Wilson, R. (1971) "Stable coalition proposals in majority-rule voting."J. of Economic Theory3: 254-271.