Existence of solution to <i>n</i>-person noncooperative games and minimax regret equilibria with set payoffs
Yu Zhang, Tao Chen, Shih-sen Chang
Abstract
In this paper, by virtue of the Kakutani–Fan–Glicksberg fixed point theorem and a nonlinear scalarization function, we first obtain an existence theorem of general n-person noncooperative games problems with set payoffs. Then, we also obtain existence theorems of minimax regret equilibria and ϵ-minimax regret equilibria with scalar set payoffs. Some examples are given to illustrate our results.
Topics & Concepts
MathematicsRegretMinimaxMathematical economicsMinimax theoremSet (abstract data type)Fixed pointFixed-point theoremApplied mathematicsDiscrete mathematicsMathematical analysisComputer scienceStatisticsProgramming languageOptimization and Variational AnalysisFixed Point Theorems AnalysisNonlinear Differential Equations Analysis