Open AccessEquilibria in symmetric games: Theory and applications
Author(s) -
Hefti Andreas
Publication year - 2017
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te2151
Subject(s) - differentiable function , mathematical economics , uniqueness , nash equilibrium , set (abstract data type) , scope (computer science) , symmetric equilibrium , computer science , boundary (topology) , game theory , equilibrium selection , mathematics , repeated game , pure mathematics , mathematical analysis , programming language
This article presents a new approach to analyze the equilibrium set of symmetric, differentiable games by separating multiple symmetric equilibria and asymmetric equilibria. This separation allows the investigation of, for example, how various parameter constellations affect the scope for multiple symmetric or asymmetric equilibria, or how the equilibrium set depends on the nature of the strategies. The approach is particularly helpful in applications because (i) it allows the complexity of the uniqueness problem to be reduced to a two‐player game, (ii) boundary conditions are less critical compared to standard procedures, and (iii) best replies need not be everywhere differentiable. The usefulness of the separation approach is illustrated with several examples, including an application to asymmetric games and to a two‐dimensional price‐information game.