Abstract
n-person (n − 1)-quota-games where the quotas are positive for certain n − 1 (strong) players and negative for the remaining (weak) player, are discussed. Normative solutions predicted by the Core,the Kernel, the Bargaining Set, the Competitive Bargaining Set, and by the Shapley Value are presented and exemplified.
Each of twelve groups of subjects participated in a four-person and a five-person (n − 1)-quota games with one weak player. The weak player was always excluded from the ratified coalition. The division of payoffs among the strong players was more egalitarian than the Kernel solution but less egalitarian than the Shapley value. The Core and the Bargaining Sets were fully supported for the two strongest players, but less supported for the other players. Analyses of the bargaining process confirmed a dynamic interpretation of the Bargaining Set Theory.
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Bibliography
Aumann, R. J.and Maschler, M., ‘The Bargaining Set for Cooperative Games’, in M. Dresher, L. S. Shapley, and A. W. Tucker (eds.), Advances in Game Theory, Princeton University Press, Princeton, N.J., 1964.
Caplow, T., Two Against One: Coalitions in Triads, Prentince Hall, Englewood Cliffs, N.J. 1968.
Davis M. and Maschler, M., ‘The Kernel of a Cooperative Game’, Naval Research Logistics Quarterly 12, (1965) 223–259.
Gamson, W. A., ‘Experimental Studies of Coalition Formation’, in L. Berkowitz (ed.), Advances in Experimental Social Psychology, Vol. 1, Academic Press, New-York, 1964.
Gillies, D. B., Some Theorems on n-Person Games, Ph.D. Thesis, Department of Mathematics, Princeton University, Princeton, N.J., 1953.
Horowitz, A. D., ‘The Competitive Bargaining Set for Cooperative n-Person Games’, Journal of Mathematical Psychology 10 (1973), 265–289 (Erratum: 11 (1974) 161).
Horowitz, A. D. and Rapoport, Am, Test of the Kernel and Two Bargaining Set Models in Four- and Five-Person Games, in An. Rapoport (ed.), Game Theory as a Theory of Conflict Resolution, D. Reidel Publishing Company, Dordrecht, Holland, 1974.
Kahan, J. P. and Rapoport, Am., ‘Test of the Bargaining Set and Kernel Models in Three-Person Games’, in An. Rapoport (ed.), Game Theory as a Theory of Conflict Resolution, D. Reidel Publishing Company, Dordrecht, Holland, 1974.
Maschler, M., ‘n-Person Games with Only 1, n − 1, and n-Person Permissible Coalitions’, Journal of Mathematical Analysis and Applications 6 (1963), 230–256.
Owen, G., Game Theory, W. B. Saunders, Philadelphia, PA, 1968.
Rapoport, An., ‘n-Person Game Theory’, Concepts and Applications, University of Michigan Press, Ann Arbor, 1970.
Shapley, L. S., ‘A Value for n-Person Games’, in H. W. Kuhn and A. W. Tucker (eds.), Contributions to the Theory of Games, Vol. II, Princeton University Press, Princeton, N.J., 1953.
Shubik, M., Games for Society, Business and War, Elsevier, New-York, 1975.
Thrall, R. M., ‘Game Theory and Some Interfaces with Control Theory’, in M. J. Beckmann and H. P. Kunzi (eds.), Lectures Notes in Economics and Mathematical Systems, Vol. 105, Springer-Verlag, N.Y., 1974.
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This research was performed while the author was at the University of North Carolina. The research was partially supported by a PHS Research Grant No. MH-10006 from the National Institute of Mental Health. The author thanks Professor Amnon Rapoport for helpful advice in the design of this study.
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Horowitz, A.D. A test of the Core, Bargaining Set, Kernel and Shapley models in n-person quota games with one weak player. Theor Decis 8, 49–65 (1977). https://doi.org/10.1007/BF00133086
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DOI: https://doi.org/10.1007/BF00133086