Arbeitspapier

Pure Saddle Points and Symmetric Relative Payoff Games

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.

Sprache
Englisch

Erschienen in
Series: Discussion Paper Series ; No. 500

Klassifikation
Wirtschaft
Noncooperative Games
Stochastic and Dynamic Games; Evolutionary Games; Repeated Games
Thema
Symmetric two-player games
zero-sum games
Rock-Paper-Scissors
single-peakedness
quasiconcavity
Nichtkooperatives Spiel
Evolutionäre Spieltheorie
Mathematik
Theorie

Ereignis
Geistige Schöpfung
(wer)
Duersch, Peter
Oechssler, Jörg
Schipper, Burkhard C.
Ereignis
Veröffentlichung
(wer)
University of Heidelberg, Department of Economics
(wo)
Heidelberg
(wann)
2010

DOI
doi:10.11588/heidok.00010545
Handle
URN
urn:nbn:de:bsz:16-opus-105453
Letzte Aktualisierung
10.03.2025, 11:42 MEZ

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Objekttyp

  • Arbeitspapier

Beteiligte

  • Duersch, Peter
  • Oechssler, Jörg
  • Schipper, Burkhard C.
  • University of Heidelberg, Department of Economics

Entstanden

  • 2010

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