Game theoretic simulation metamodeling using stochastic kriging

Abstract

This paper presents a new approach to the construction of game theoretic metamodels from data obtained through stochastic simulation. In this approach, stochastic kriging is used to estimate payoff functions of players involved in a game represented by a simulation model. Based on the estimated payoff functions, the players' best responses to the values of the decision variables chosen by the other players are calculated. In the approach, the concept of best response sets in the context of game theoretic simulation metamodeling is applied. These sets contain the values of the players' decision variables which cannot be excluded from being a best response and allow the identification of the potential Nash equilibria. The utilization of the approach is demonstrated with simulation examples where payoff functions are known a priori. Additionally, it is applied to data acquired by using a discrete event air combat simulation model.