Tropical Complementarity Problems and Nash Equilibria - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Discrete Mathematics Année : 2023

Tropical Complementarity Problems and Nash Equilibria

Résumé

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 et versions

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

Identifiants

Citer

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⟩
19 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More