Abstract
We consider an oligopolistic market as follows. In the market, one good is traded for money. Each oligopolist is a price setter and has the same linear cost function. Each buyer is a price taker and buys the good from oligopolists setting the lowest price. We formulate this market as a cooperative game, and consider two kinds of solution concepts, the core and a bargaining set of the game. First we show that in the monopolistic market, the core gives the monopoly price, but in the oligopolistic market, the core is empty. Second, we obtain the bargaining set of the oligopolistic market.
Similar content being viewed by others
References
Aumann, R.J.: Markets with a continuum of traders. Econometrica32, 1964, 39–50.
—: Disadvantageous monopolies. J.Econ. Theory6, 1973, 1–11.
Aumann, R.J., andM. Maschler: The bargaining set for cooperative games. Advances in Game Theory. Ed.by L.S. Shapley and A.W. Tucker. Annals of Mathematics Studies52, Princeton 1964, 443–466.
Chamberlin, E.H.: The theory of monopolistic competition. Cambridge 1933; 8th ed. Cambridge 1962.
Debreu, G., andH. Scarf: A limit theorem on the core of an economy. Intern. Econ. Rev.4, 1963, 235–246.
Fellner, W.: Competition among few — Oligopoly and similar market structure -, 1949. Reprinted by Augstus M. Kelley, 1965.
Gabszewicz, J.J., andJ.F. Mertens: An equivalence theorem for the core of an economy whose atoms are not too big. Econometrica39, 1970, 53–62.
Kaneko, M.: Note on transferable utility. Intern. J. Game Theory5, 1976, 215–219.
Levitan, R.E., andM. Shubik: Price duopoly and capacity constraints. Intern. Econ. Rev.13, 1972, 111–122.
Maschler, M.: An advantage of the bargaining set over the core. J. Econ. Theory13, 1976, 184–192.
Peleg, B.: The extended bargaining set for cooperative games without side payments. Res. Memo.44, Department of Mathematics, Hebrew University, 1969.
Postlwaite, A., andR.W. Rosenthal: Disadvantageous syndicates. J. Econ. Theory9, 1974, 324–326.
Selten, R.: A simple model of imperfect competition, where 4 are few and 6 are many. Intern. J. Game Theory2, 1973, 141–201.
Shapley, L.S., andM. Shubik: Concepts and theories of pure competition. Essays in Mathematical Economics: In Honor of Oskar Morgenstern. Ed. by M. Shubik. Princeton 1967, 63–79.
Shitovitz, B.: Oligopoly in markets with a continuum of traders. Econometrica41, 1973, 467–501.
—: On some problems arising in markets with some large traders and a continuum of traders. J.E. Theory8, 1974, 458–470.
Shubik, M.: Strategy and market structure. New York 1959.
von Neumann, J., andO. Morgenstern: Theory of games and economic behavior. Princeton 1944.
Author information
Authors and Affiliations
Additional information
The author wishes to express his thanks to Dr. Shigeo Muto for valuable discussions concerning this paper.
Rights and permissions
About this article
Cite this article
Kaneko, M. Price oligopoly as a cooperative game. Int J Game Theory 7, 137–150 (1978). https://doi.org/10.1007/BF01769186
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01769186