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arXiv · 2012.05314

Tropical complementarity problems and Nash equilibria

Xavier Allamigeon·Stéphane Gaubert·Frédéric Meunier
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Abstract

Linear complementarity programming is a generalization of linear programming which encompasses the computation of Nash equilibria for bimatrix games. While the latter problem is PPAD-complete, we show that the tropical analogue of the complementarity problem associated with Nash equilibria can be solved in polynomial time. Moreover, we prove that the Lemke--Howson algorithm carries over the tropical setting and performs a linear number of pivots in the worst case. A consequence of this result is a new class of (classical) bimatrix games for which Nash equilibria computation can be done in polynomial time.

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Xavier Allamigeon, Stéphane Gaubert, Frédéric Meunier. 2020-12-09. Tropical complementarity problems and Nash equilibria. https://arxiv.org/abs/2012.05314

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