Environmental game modeling with uncertainties.

Ji, Ying; Qu, Shaojian; Chen, Fuxing

We model environmental games with stochastic data based on an imprecise distribution which is assumed to be attached to an a-priori known set. Our model is different from previous games where the probability distribution of the uncertain data is precisely given. Our model is also different from the robust games which presents a robust optimization approach to game models with the uncertain data in a compact convex set without probabilistic information which can lead to overly conservative solutions. A distributionally robust approach is used to cope with our setting in the games by combining the stochastic optimization and robust optimization approaches which can be termed as the distributionally robust environmental games. We show that the existence of an equilibrium for the distributionally robust environmental games under mild assumptions. The computation method for equilibrium, with the first- and second-information about the probability of uncertain data, can be reformulated as a semidefinite programming problem which can be tractably realized. Numerical tests are given to show the efficiency of the proposed methods.

ROBUST optimization; SEMIDEFINITE programming; CONVEX sets; STOCHASTIC programming; DATA distribution; DATABASES; PROBABILISTIC databases

Discrete & Continuous Dynamical Systems - Series S, 2019, Vol 12, Issue 4/5, p989

1937-1632

Academic Journal

10.3934/dcdss.2019067