Deep Fictitious Play for Games with Continuous Action Spaces

Fictitious play has been a classic algorithm to solve two-player adversarial games with discrete action spaces. In this work we develop an approximate extension of fictitious play to two-player games with high-dimensional continuous action spaces. We use generative neural networks to approximate players' best responses while also learning a differentiable approximate model to the players' rewards given their actions. Both these networks are trained jointly with gradient-based optimization to emulate fictitious play. We explore our approach in zero-sum games, non zero-sum games and security game domains.