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Journal Articles SIAM Journal on Discrete Mathematics Year : 2023

Tropical Complementarity Problems and Nash Equilibria

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.

Dates and versions

hal-04355016 , version 1 (20-12-2023)

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Xavier Allamigeon, Stéphane Gaubert, Frédéric Meunier. Tropical Complementarity Problems and Nash Equilibria. SIAM Journal on Discrete Mathematics, 2023, 37 (3), pp.1645-1665. ⟨10.1137/21M1446861⟩. ⟨hal-04355016⟩
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