Evolution Strategies for Approximate Solution of Bayesian Games

We address the problem of solving complex Bayesian games, characterized by high-dimensional type and action spaces, many (> 2) players, general-sum payoffs. Our approach applies to symmetric one-shot with no given analytic structure. represent agent strategies in parametric form as neural networks, apply natural evolution (NES) [wierstra2014natural] for deep model optimization. For pure equilibrium computation, we formulate bi-level optimization, employ NES an iterative algorithm implement both inner-loop best response optimization outer-loop regret minimization. In simple games including first- second-price auctions, it is capable recovering known solutions. mixed adopt incremental strategy generation framework, generator producing a finite sequence approximate best-response strategies. then calculate equilibria over this set via model-based process. Both our computation methods efficiently search functional space, only black-box simulation access noisy payoff samples. experimentally demonstrate efficacy all on two simultaneous sealed-bid auction distinct distributions, observe that solutions exhibit qualitatively different behavior these environments.