EQUIVALENT SECOND ORDER CONE PROGRAMS FOR DISTRIBUTION-ALLY ROBUST ZERO-SUM GAMES

Vikram Vikas , Ayush Agarwal , Navnit Yadav , Abdel Lisser (1)

1 L2S - Laboratoire des signaux et systèmes

We consider a two-player zero-sum game with random linear constraints. The probability distributions of the random constraint vectors are partially known. The available information with respect to the distribution is based mainly on the first two moments. In this vein, we formulate the random linear constraints as distributionally robust chance constraints. We consider three different types of moments based uncertainty sets. For each uncertainty set, we show that a saddle point equilibrium of the game can be obtained from the optimal solutions of a primal-dual pair of second order cone programs. We illustrate our theoretical results on randomly generated game instances of different sizes.

Mots clés: Distributionally robust chance constraints; Zero-sum game; Saddle point

Domaines: Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Vikram Vikas, Ayush Agarwal, Navnit Yadav, Abdel Lisser. EQUIVALENT SECOND ORDER CONE PROGRAMS FOR DISTRIBUTION-ALLY ROBUST ZERO-SUM GAMES. 2021. ⟨hal-03106386⟩