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Abstract

This paper deals with the question of coalition formation inn-person cooperative games. Two abstract game models of coalition formation are proposed. We then study the core and the dynamic solution of these abstract games. These models assume that there is a rule governing the allocation of payoffs to each player in each coalition structure called a payoff solution concept. The predictions of these models are characterized for the special case of games with side payments using various payoff solution concepts such as the individually rational payoffs, the core, the Shapley value and the bargaining set M1 (i). Some modifications of these models are also discussed.

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References

  • Anderson, S.L., andE.A. Traynor: An application of the Aumann-Maschlern-person cooperative game. Recent Advances in Game Theory. Ed. by M. Maschler. Princeton 1962, 265–270.

  • Aumann, R.J., andJ. Dreze: Cooperative games with coalition structures. International Journal of Game Theory3, 1974, 217–237.

    Google Scholar 

  • Aumann, R.J., andM. Maschler: The bargaining set for cooperative games. Annals of Mathematics Study52, 1964, 443–476.

    Google Scholar 

  • Bondareva, O.N.: Theory of the core in then-person game. Leningrad State University Vestnik L. G. U. 13, 1962, 141–142. (In Russian)

    Google Scholar 

  • —: Some applications of linear programming methods to the theory of cooperative games. Problemy Kibernetiki10, 1963, 119–139. (In Russian)

    Google Scholar 

  • Brams, S.J.: Paradoxes in Politics. New York 1976.

  • Davis, M., andM. Maschler: Existence of stable payoff configurations for cooperative games. Essays in Mathematical Economics in Honor of Oskar Morgenstern. Ed. by M. Shubik. Princeton 1967, 39–52.

  • Gamson, W.A.: A theory of coalition formation. American Sociological Review26, 1961, 373–382.

    Google Scholar 

  • Gillies, D.B.: Solutions to general non-zero-sum games. Annals of Mathematics Study40, 1959, 47–85.

    Google Scholar 

  • Harary, F.: Graph Theory. Massachusetts 1959.

  • Kalai, E., E.A. Pazner andD. Schmeidler: Collective choice correspondences as admissible outcomes of social bargaining processes. Econometrica44, 1976, 223–240.

    Google Scholar 

  • Lucas, W.F.: A game with no solution. Bull. Amer. Math. Soc.74, 1968, 237–239.

    Google Scholar 

  • —: A proof that a game may not have a solution. Trans Amer. Math. Soc.137, 1969, 219–229.

    Google Scholar 

  • Lucas, W.F., andJ.C. Maceli: Discrete partition function games. Game Theory and Political Science. Ed. by P. Ordeshook. New York 1978, 191–213.

  • Peleg, B.: Existence theorem for the bargaining set. Essays in Mathematical Economics in Honor of Oskar Morgenstern. Ed. by M. Shubik. Princeton 1967, 53–76.

  • Riker, W.H., andP. Ordeshook: An Introduction to Positive Political Theory. New York 1973.

  • Shapley, L.S.: A value for n-person games. Annals of Mathematics Study28, 1953, 307–317.

    Google Scholar 

  • —: Simple games: An outline of the descriptive theory. Behavioral Science7, 1962, 59–66.

    Google Scholar 

  • —: On balanced sets and cores. Naval Research Logistics Quarterly14, 1967, 453–460.

    Google Scholar 

  • Shapley, L.S., andM. Shubik: A method for evaluating the distribution of power in a committee system. Amer. Political Science Review48, 1954, 787–792.

    Google Scholar 

  • Shenoy, P.P.: A dynamic solution concept for abstract games. Mathematics Research Center, Technical Summary Report No. 1804, University of Wisconsin, Madison 1977a.

  • -: On game theory and coalition formation. School of Operations Research and Industrial Engineering, Cornell University, Technical Report No. 342, New York, 1977b.

  • —: On coalition formation in simple games: A mathematical analysis of Caplow's and Gamson's theories. Journal of Mathematical Psychology18, 1978, 177–194.

    Google Scholar 

  • Thrall, R.M., andW.F. Lucas: n-person games in partition function form. Naval Research Logistics Quarterly10, 1963, 281–298.

    Google Scholar 

  • Von Neumann, J., andO. Morgenstern: Theory of Games and Economic Behavior. Princeton 1944, 3rd edition, 1953.

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This research was supported in part by the Office of Naval Research under Contract N00014-75-C-0678 and the National Science Foundation under Grants MPS75-02024 and MCS77-03984 at Cornell University and also by the United States Army under Contract No. DAAG-29-75-C-0024 and the National Science Foundation under Grant No. MCS75-17385 A01 at the University of Wisconsin at Madison. The author is grateful to Professor William F. Lucas under whose guidance the research was conducted and to Professor Louis J. Billera for many helpful discussions.

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Shenoy, P.P. On coalition formation: a game-theoretical approach. Int J Game Theory 8, 133–164 (1979). https://doi.org/10.1007/BF01770064

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  • DOI: https://doi.org/10.1007/BF01770064

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