Approaching the Overbidding Puzzle in All-Pay Auctions: Explaining Human Behavior through Bayesian Optimization and Equilibrium Learning

It is an established fact in behavioral economics that in lab experiments of auctions, human subjects do not adhere to the risk-neutral Bayesian Nash equilibria of such games. Several attempts at explaining this Overbidding Puzzle focus on the bidders' psychology and suggest they may have parametrized utility functions that differ from the risk-neutral payoff. However, analytical equilibria of the resulting modified games are generally not available. Consequently, it has been difficult to identify the specific parameters and assess the merits of these proposed modifications in explaining empirical observations. With recent advances in equilibrium learning, it has become tractable to compute approximations of Bayesian Nash equilibria. Building on these advances and Bayesian optimization, we propose a novel regression framework to infer unobserved parameters of Bayesian games from behavioral data. We apply our method to two data sets of human bidding behavior in all-pay auctions. For the first time, this makes it possible to directly compare the goodness-of-fit of several proposed qualitative explanations of overbidding.