Computing Bayes–Nash Equilibrium Strategies in Auction Games via Simultaneous Online Dual Averaging

Determining equilibria in auction games is computationally hard in general, and no exact solution theory is known. We introduce an algorithmic framework in which we discretize type and action space and then learn distributional strategies via online optimization algorithms. We show that the equilibrium of the discretized auction game approximates an equilibrium in the continuous game. In a wide variety of auction games, we provide empirical evidence that the approach approximates the analytical (pure) Bayes–Nash equilibrium closely. In standard models in which agents are symmetric, we find equilibrium in seconds. The method allows for interdependent valuations and different types of utility functions, and it can be used to find equilibrium in auction markets and beyond.