Abstract
This paper is concerned with the analysis of a Nash equilibrium of a noncooperative game. It can be shown that, without complete information about the other players' objectives or interests, the group of players, as a whole, can reach a Nash equilibrium by adopting a class of adaptive expectation and dynamic adjustment processes. It is shown that, if the expectation and adjustment processes are made continuously, the stability of the overall dynamic process is independent of the specific mechanisms of the expectation and the adjustment, but depends on the properties of each player's objective or payoff function. If, however, expectation and adjustment processes are made at discrete time intervals, the stability of the discrete process depends on the speed of adjustment chosen by each player.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brito, D. L.,A Dynamic Model of Armament Races, International Economic Review, Vol. 13, pp. 359–375, 1972.
Ruffin, R. J.,Cournot Oligopoly and Competitive Behavior, Review of Economic Studies, Vol. 38, pp. 493–502, 1971.
Fisher, F. M.,The Stability of the Cournot Oligopoly Solution, Review of Economic Studies, Vol. 28, pp. 125–135, 1961.
Friedman, J.,Oligopoly and the Theory of Games, North-Holland Publishing Company, Amsterdam, Holland, 1977.
Osborne, D.,The Duopoly Game: Output Variations, American Economic Review, Vol. 61, pp. 538–560, 1971.
Simaan, M., andCruz, J. B.,Nash Equilibrium Strategies for the Problem of Armament Race and Control, Management Science, Vol. 22, pp. 96–105, 1975.
Luce, R. D., andRaiffa, H.,Games and Decisions, John Wiley and Sons, New York, New York, 1957.
Nash, J.,Noncooperative Games, Annals of Mathematics, Vol. 54, pp. 286–295, 1951.
Kakutani, S.,A Generalization of Brouwer's Fixed-Point Theorem, Duke Mathematical Journal, Vol. 8, pp. 457–458, 1941.
Cournot, A.,Researches into the Mathematical Principles of the Theory of Wealth, Translation by N. T. Bacon, The Macmillan Company, New York, New York, 1897.
Okuguchi, K.,Expectations and Stability in Oligopoly Models, Springer-Verlag, Berlin, Germany, 1976.
Murata, Y.,Mathematics for Stability and Optimization of Economic Systems, Academic Press, New York, New York, 1977.
Brito, O. L., andIntriligator, M. D.,A Fixed-Point Approach to Multiagent Adaptive Control, Annals of Economic and Social Measurement, Vol. 6, pp. 137–145, 1977.
Nerlove, M.,Distributed Lags and Demand Analysis, Agricultural Handbook No. 141, US Government Printing office, Washington, DC, 1958.
Cagan, P. H.,The Monetary Dynamics of Hyperinflation, Studies in the Quantity Theory of Money, Edited by M. Friedman, University of Chicago Press, Chicago, Illinois, 1956.
Waud, R.,Small Sample Bias Due to Misspecification in the Partial Adjustment and Adaptive Expectation Models, Journal of the American Statistical Association, Vol. 61, pp. 1130–1152, 1966.
Griliches, Z.,Distributed Lags: A Survey, Econometrica, Vol. 35, pp. 16–49, 1967.
Author information
Authors and Affiliations
Additional information
Communicated by M. D. Intriligator
This research was supported by ONR Contract No. N00014-75-C-0738. The authors are indebted to the referee for several valuable comments and suggestions for improvement.
Rights and permissions
About this article
Cite this article
Namatame, A., Tse, E. Adaptive expectations and dynamic adjustment in noncooperative games with incomplete information. J Optim Theory Appl 34, 243–261 (1981). https://doi.org/10.1007/BF00935475
Issue Date:
DOI: https://doi.org/10.1007/BF00935475