Pure strategy equilibria in symmetric two-player zero-sum games
We observe that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for existenc...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
August 2012
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| In: |
International journal of game theory
Year: 2012, Volume: 41, Issue: 3, Pages: 553-564 |
| ISSN: | 1432-1270 |
| DOI: | 10.1007/s00182-011-0302-x |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1007/s00182-011-0302-x Verlag, Volltext: http://link.springer.com/10.1007/s00182-011-0302-x 
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| Author Notes: | Peter Duersch, Jörg Oechssler, Burkhard C. Schipper |
| Summary: | We observe that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for existence are provided. Our findings extend to general two-player zero-sum games using the symmetrization of zero-sum games due to von Neumann. We point out that the class of symmetric twoplayer zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of finite population evolutionary stable strategies. |
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| Item Description: | Gesehen am 29.11.2018 First online: 15 September 2011 |
| Physical Description: | Online Resource |
| ISSN: | 1432-1270 |
| DOI: | 10.1007/s00182-011-0302-x |