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Bounds on the number of ESSs of a matrix game
journal contribution
posted on 2023-06-08, 08:40 authored by Mark BroomIt 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 a 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(a) with useful regularity properties, and bounds are found for both f(a) and the value a*, 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.
History
Publication status
- Published
Journal
Mathematical BiosciencesISSN
0025-5564Publisher
ElsevierExternal DOI
Issue
2Volume
167Page range
163-175ISBN
0025-5564Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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