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Pareto optimum by independent trials

Published online by Cambridge University Press:  17 April 2009

D.J. Gates  and
J.A. Rickard
D.J. Gates
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria.
J.A. Rickard
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria.
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Abstract

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We consider a method by which players in a continuous N-person game can arrive at a Pareto optimal solution by a trial process. The process has a number of novel features. Firstly, it is assumed that the players do not know the payoff functions. Secondly, the players are assumed to act quite independently. In spite of this lack of information and lack of cooperation, the players eventually arrive at what is usually regarded as a cooperative solution. The process is a model of the accounting procedures used by firms, and the results predict approach to an equilibrium state of a market model. Proofs are given only in outline here.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 2 , April 1975 , pp. 259 - 265
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Gates, D.J., Rickard, J.A. and Wilson, D.J., “Properties of a price-adjustment process”, (in preparation).Google Scholar
[2]Shubik, Martin, Strategy and market structure; competition, oligopoly, and the theory of games (John Wiley & Sons, New York, London, 1959).Google Scholar
[3]Weinberg, Robert S., “The uses and limitations of mathematical models for market planning”, Mathematical models and methods in marketing, 3–34 (Irwin Series in Quantitative Analysis for Business. Irwin, Homewood, Illinois, 1961).Google Scholar