Simple equilibria in finite games with convexity properties

• Autorzy: Tadeusz Radzik , Piotr Więcek
• Języki publikacji: EN

Abstrakty

EN

This review paper gives a characterization of non-coalitional zero-sum and non-zero-sum games with finite strategy spaces and payoff functions having some concavity or convexity properties. The characterization is given in terms of the existence of two-point Nash equilibria, that is, equilibria consisting of mixed strategies with spectra consisting of at most two pure strategies. The structure of such simple equilibria is discussed in various cases. In particular, many of the results discussed can be seen as discrete counterparts of classical theorems about the existence of pure (or "almost pure") Nash equilibria in continuous concave (convex) games with compact convex spaces of pure strategies. The paper provides many examples illustrating the results presented and ends with four related open problems.

Kategorie tematyczne

• 91A10: Noncooperative games
• 91A05: 2-person games
• 91B52: Special types of equilibria
• 91A06: n -person games, n > 2

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2015
• Tom: 42
• Numer: 1
• Strony: 83-109

Daty

wydano

2015

Twórcy

autor

Tadeusz Radzik

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Piotr Więcek

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Identyfikatory

DOI

10.4064/am42-1-6