Advertisement

International Journal of Game Theory

, Volume 7, Issue 3–4, pp 137–150 | Cite as

Price oligopoly as a cooperative game

  • M. Kaneko
Papers

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.

Keywords

Cost Function Economic Theory Game Theory Lower Price Cooperative Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aumann, R.J.: Markets with a continuum of traders. Econometrica32, 1964, 39–50.Google Scholar
  2. —: Disadvantageous monopolies. J.Econ. Theory6, 1973, 1–11.Google Scholar
  3. 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.Google Scholar
  4. Chamberlin, E.H.: The theory of monopolistic competition. Cambridge 1933; 8th ed. Cambridge 1962.Google Scholar
  5. Debreu, G., andH. Scarf: A limit theorem on the core of an economy. Intern. Econ. Rev.4, 1963, 235–246.Google Scholar
  6. Fellner, W.: Competition among few — Oligopoly and similar market structure -, 1949. Reprinted by Augstus M. Kelley, 1965.Google Scholar
  7. 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.Google Scholar
  8. Kaneko, M.: Note on transferable utility. Intern. J. Game Theory5, 1976, 215–219.Google Scholar
  9. Levitan, R.E., andM. Shubik: Price duopoly and capacity constraints. Intern. Econ. Rev.13, 1972, 111–122.Google Scholar
  10. Maschler, M.: An advantage of the bargaining set over the core. J. Econ. Theory13, 1976, 184–192.Google Scholar
  11. Peleg, B.: The extended bargaining set for cooperative games without side payments. Res. Memo.44, Department of Mathematics, Hebrew University, 1969.Google Scholar
  12. Postlwaite, A., andR.W. Rosenthal: Disadvantageous syndicates. J. Econ. Theory9, 1974, 324–326.Google Scholar
  13. Selten, R.: A simple model of imperfect competition, where 4 are few and 6 are many. Intern. J. Game Theory2, 1973, 141–201.Google Scholar
  14. 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.Google Scholar
  15. Shitovitz, B.: Oligopoly in markets with a continuum of traders. Econometrica41, 1973, 467–501.Google Scholar
  16. —: On some problems arising in markets with some large traders and a continuum of traders. J.E. Theory8, 1974, 458–470.Google Scholar
  17. Shubik, M.: Strategy and market structure. New York 1959.Google Scholar
  18. von Neumann, J., andO. Morgenstern: Theory of games and economic behavior. Princeton 1944.Google Scholar

Copyright information

© Physica-Verlag 1978

Authors and Affiliations

  • M. Kaneko
    • 1
  1. 1.Institute of Socio-Economic PlanningUniversity of TsukubaIbaraki-kenJapan

Personalised recommendations