Game theory models strategic interactions among agents, focusing on situations of conflict and offering various solution concepts, known as equilibria. Bayesian games consider situations in which players have private types and act and receive payoffs based on those types. The problem of computing Bayesian Nash equilibria has been thoroughly investigated, and solutions for various Bayesian games have been applied to many real-world applications. From a designer’s point of view, the inverse problem of constructing a game that has a particular equilibrium value, yielding a certain payoff for each player and each of its possible types, is also of interest as it can provide methods for incentivizing agents towards certain decisions. In this paper, we address this problem in Bayesian games by using a genetic programming approach to evolve payoff functions that construct a Bayesian game given a specified equilibrium configuration and corresponding payoff values.
Suciu et al. (Mon,) studied this question.