Authors:
Vikas Vikram Singh
1
;
Oualid Jouini
2
and
Abdel Lisser
1
Affiliations:
1
Universite Paris Sud XI, France
;
2
Ecole Centrale Paris, France
Keyword(s):
Chance-Constrained Game, Nash Equilibrium, Normal Distribution, Cauchy Distribution, Nonlinear Complementarity Problem, Linear Complementarity Problem.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Game Theory
;
Knowledge Discovery and Information Retrieval
;
Knowledge-Based Systems
;
Methodologies and Technologies
;
Operational Research
;
Optimization
;
Stochastic Optimization
;
Symbolic Systems
Abstract:
We consider a two player bimatrix game where the entries of each player’s payoff matrix are independent random variables following a certain distribution. We formulate this as a chance-constrained game by considering that the payoff of each player is defined by using a chance-constraint. We consider the case of normal and Cauchy distributions. We show that a Nash equilibrium of the chance-constrained game corresponding to normal distribution can be obtained by solving an equivalent nonlinear complementarity problem. Further if the entries of the payoff matrices are also identically distributed with non-negative mean, we show that a strategy pair, where each player’s strategy is the uniform distribution on his action set, is a Nash equilibrium of the chance-constrained game. We show that a Nash equilibrium of the chance-constrained game corresponding to Cauchy distribution can be obtained by solving an equivalent linear complementarity problem.