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On the Existence of Stationary Nash Equilibria for Mean Payoff Games on Graphs
Authors: Lozovanu Dmitrii, Stefan Pickl
Keywords: mean payoff game, pure stationary strategy, mixed stationary strategy, stationary Nash equilibrium
– 0.14 Mb
Keywords: mean payoff game, pure stationary strategy, mixed stationary strategy, stationary Nash equilibrium
Abstract
In this paper we extend the classical concept of positional strategies for a mean payoff game to a general mixed stationary strategy approach, and prove the existence of mixed stationary Nash equilibria for an arbitrary $m$-player mean payoff game on graphs. Traditionally, a positional strategy represents a pure stationary strategy in a classical mean payoff game, where a Nash equilibrium in pure stationary strategies in general may not exist. Based on a constructive proof of the existence of specific equilibria for an $m$-player mean payoff game we propose a new approach for determining the optimal mixed stationary strategies. Additionally we characterize and extend the general problem of the existence of pure stationary Nash equilibria for some special classes of mean payoff games.Dmitrii Lozovanu
Institute of Mathematics and Computer Science,
Moldova State University,
5 Academiei str., Chisinau, MD−2028, Moldova
E-mail:
Stefan Pickl
Institute for Theoretical Computer Science,
Mathematics and Operations Research,
Universit¨at der Bundeswehr,M¨unchen,
85577 Neubiberg-M¨unchen, Germany,
E-mail:
Institute of Mathematics and Computer Science,
Moldova State University,
5 Academiei str., Chisinau, MD−2028, Moldova
E-mail:
Stefan Pickl
Institute for Theoretical Computer Science,
Mathematics and Operations Research,
Universit¨at der Bundeswehr,M¨unchen,
85577 Neubiberg-M¨unchen, Germany,
E-mail:
DOI
https://doi.org/10.56415/basm.y2023.i2.p41Fulltext
– 0.14 Mb
Contents
- The Second Hankel Determinant for k-symmetrical Functions
- Relative Separation Axioms via Semi-Open Sets
- Growth Properties of Solutions to Higher Order Complex Linear Differential Equations with Analytic Coefficients in the Annulus
- On T-nilpotence of a matrix set
- On the Existence of Stationary Nash Equilibria for Mean Payoff Games on Graphs
- Global Asymptotic Stability of Generalized Homogeneous Dynamical Systems
- The linear Fredholm integral equations with functionals and parameters
- B-spline collocation method for solving Fredholm integral equations with discontinuous right-hand side
- On recursive 1-differentiability of the quasigroup prolongations
- Zero-Order Markov Processes with Multiple Final Sequences of States
