【摘 要】
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In this talk, we consider a class of n-person noncooperative games, where the utility function of every player is given by a homogeneous polynomial defined
【机 构】
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TianjinUniversity
【出 处】
：
2016年张量和矩阵学术研讨会(International conference on Tensor, Matrix a
论文部分内容阅读
In this talk, 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 util-ity 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 mul-tilinear game is equivalent to finding a solution of the resulted tensor complementarity problem. Especially, we present an explicit relationship between the solutions of the mul-tilinear 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.
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