Formulating an n-person noncooperative game as a tensor complementarity problem

Zheng-Hai Huang () and Liqun Qi ()
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Zheng-Hai Huang: Tianjin University
Liqun Qi: The Hong Kong Polytechnic University

Computational Optimization and Applications, 2017, vol. 66, issue 3, No 7, 557-576

Abstract: Abstract In this paper, we consider a class of n-person noncooperative games, where the utility function of every player is given by a homogeneous polynomial defined by the payoff tensor of that player, which is a natural extension of the bimatrix game where the utility function of every player is given by a quadratic form defined by the payoff matrix of that player. We will call such a problem the multilinear game. We reformulate the multilinear game as a tensor complementarity problem, a generalization of the linear complementarity problem; and show that finding a Nash equilibrium point of the multilinear game is equivalent to finding a solution of the resulted tensor complementarity problem. Especially, we present an explicit relationship between the solutions of the multilinear game and the tensor complementarity problem, which builds a bridge between these two classes of problems. We also apply a smoothing-type algorithm to solve the resulted tensor complementarity problem and give some preliminary numerical results for solving the multilinear games.

Keywords: Game theory; n-person noncooperative game; Nash equilibrium; Bimatrix game; Tensor complementarity problem (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (31)

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DOI: 10.1007/s10589-016-9872-7

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