Bounds on the number of ESSs of a matrix game

Broom, Mark (2000) Bounds on the number of ESSs of a matrix game. Mathematical Biosciences, 167 (2). pp. 163-175. ISSN 0025-5564

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Abstract

It is well known that for any evolutionary game there may be more than one evolutionarily stable strategy (ESS). In general, the more ESSs there are, the more difficult it is to work out how the population will behave (unless there are no ESSs at all). If a matrix game has an ESS which allows all possible pure strategies to be played, referred to as an internal ESS, then no other ESS can exist. In fact, the number of ESSs possible is highly dependent upon how many of the pure strategies each allow to be played, their support size. It is shown that if α is the ratio of the mean support size to the number of pure strategies n, then as n tends to infinity the greatest number of ESSs can be represented by a continuous function f(α) with useful regularity properties, and bounds are found for both f(α) and the value α∗, where it attains its maximum. Thus we can obtain a limit on the complexity of any particular system as a function of its mean support size.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Mark Broom
Date Deposited: 06 Feb 2012 21:03
Last Modified: 10 Jul 2012 13:21
URI: http://sro.sussex.ac.uk/id/eprint/29337
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