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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.

CC BY-NC-ND 4.0

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Paper citation in several formats:
Singh, V.; Jouini, O. and Lisser, A. (2016). A Complementarity Problem Formulation for Chance-constraine Games. In Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - ICORES; ISBN 978-989-758-171-7; ISSN 2184-4372, SciTePress, pages 58-67. DOI: 10.5220/0005754800580067

@conference{icores16,
author={Vikas Vikram Singh. and Oualid Jouini. and Abdel Lisser.},
title={A Complementarity Problem Formulation for Chance-constraine Games},
booktitle={Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - ICORES},
year={2016},
pages={58-67},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005754800580067},
isbn={978-989-758-171-7},
issn={2184-4372},
}

TY - CONF

JO - Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - ICORES
TI - A Complementarity Problem Formulation for Chance-constraine Games
SN - 978-989-758-171-7
IS - 2184-4372
AU - Singh, V.
AU - Jouini, O.
AU - Lisser, A.
PY - 2016
SP - 58
EP - 67
DO - 10.5220/0005754800580067
PB - SciTePress