HAL CCSD
EQUIVALENT SECOND ORDER CONE PROGRAMS FOR DISTRIBUTION-ALLY ROBUST ZERO-SUM GAMES
Vikas, Vikram
Agarwal, Ayush
Yadav, Navnit
Lisser, Abdel
Laboratoire des signaux et systèmes (L2S) ; CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)
hal-03106386
https://centralesupelec.hal.science/hal-03106386
https://centralesupelec.hal.science/hal-03106386/document
https://centralesupelec.hal.science/hal-03106386/file/DRO_Zeo-sum.pdf
https://centralesupelec.hal.science/hal-03106386
2021
en
Distributionally robust chance constraints
Zero-sum game
Saddle point
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
info:eu-repo/semantics/preprint
Preprints, Working Papers, ...
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.
2021-01-11
info:eu-repo/semantics/OpenAccess