Regret-Minimizers and Convergence to Price-Taking

This paper studies a variety of forms of regret minimization as the criteria with which traders choose their bids/asks in a double auction. Unlike the expected utility maximizers that populate typical market models, these traders do not determine their actions using a single prior. The analysis proves that minimax regret traders will not converge to price-taking as the number of traders in the market increases, contrary to standard economic intuition. In fact, minimax regret traders’ bids and asks are invariant to the number of other traders in the market. However, not all regret-based decision rules fail to respond to market size. Introducing priors over some part of the decision problem to minimize expected maximum regret, or multiple priors to minimize maximum expected regret, have different effects. The robustness of the sealed bid double auction is limited by the need to avoid priors that eliminate traders incentive to truthfully reveal their redemption values.