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Extended optima and equilibria for continuous games. I. General results

Published online by Cambridge University Press:  17 February 2009

D. J. Gates and
M. Westcott
D. J. Gates
Affiliation:
C. S. I. R. O. Division of Mathematics and Statistics, P. O. Box 1965, Canberra, ACT 2601
M. Westcott
Affiliation:
C. S. I. R. O. Division of Mathematics and Statistics, P. O. Box 1965, Canberra, ACT 2601
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In this, the first of three papers, we examine conditions, derived previously, which specify the equilibrium solutions of an adjustment process for N players engaged in a game with continuous (in fact, continuously differentiable) payoff functions, where each player's strategy is to choose a single real number. It is equivalent to the basic form of quantity-variation competition between N firms. The conditions are related to a new optimum which takes account of the ability of firms, or coalitions of firms, to discipline another firm that tries to increase its own profit. Closely related optima are also introduced and analysed. The new optima occupy N-dimensional regions in the strategy space, and contain the optima of Cournot, Pareto, von-Neumann and Morgenstern, and Nash as special cases.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 3 , January 1981, pp. 291 - 307
Copyright
Copyright © Australian Mathematical Society 1981

References

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