Pure saddle points and symmetric relative payoff games

• Verfasst von: Dürsch, Peter [VerfasserIn]
• Verfasst von: Oechssler, Joerg [VerfasserIn]
• Verfasst von: Schipper, Burkhard [VerfasserIn]
• Titel: Pure saddle points and symmetric relative payoff games
• Verf.angabe: Peter Duersch; Jörg Oechssler; Burkhard C. Schipper
• Verlagsort: Heidelberg
• Verlag: Universitätsbibliothek der Universität Heidelberg
• E-Jahr: 2010
• Jahr: February 21, 2010
• Umfang: 1 Online-Ressource
• Gesamttitel/Reihe: Discussion paper series / Universität Heidelberg, Department of Economics ; No. 500
• Fussnoten: Online publiziert: 2010
• ComputerInfo: Systemvoraussetzungen: Acrobat Reader.
• URN: urn:nbn:de:bsz:16-opus-105453
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Symmetric two-player games
• Sach-SW: zero-sum games
• Sach-SW: Rock-Paper-Scissors
• Sach-SW: single-peakedness
• Sach-SW: quasiconcavity
• Form-SW: Arbeitspapier
• Form-SW: Graue Literatur
• K10plus-PPN: 623037912
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors game. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure saddle point. Further sufficient conditions for existence are provided. We apply our theory to a rich collection of examples by noting that the class of symmetric two-player 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 a finite population evolutionary stable strategies.