Convergence to Price-Taking by Regret-Minimizers in k-Double Auctions

Abstract

This paper investigates robustness of price-taking behavior in the private value k-double auction under Knightian uncertainty. A decision problem involves Knightian uncertainty if the agent knows the outcome in each possible state of the world for all available actions, but does not know each state's probability. In our model, traders face Knightian uncertainty regarding other traders' strategies, and possibly the distribution of their redemption values as well. One of the decision rules available to a decision-maker facing Knightian uncertainty is minimax regret. Unlike expected utility maximizers, minimax regret traders eschew all priors. We find that minimax regret traders will not converge to price-taking behavior even as the number of traders in the market increases. Since minimax regret traders will not converge to price-taking, the outcome in a double auction market populated by such agents will not converge to efficiency as the size of the market grows. However, not all regret-based decision rules fail to respond to market size, as minimax regret does. Introducing priors over some part of the decision problem to minimize expected maximum regret, or multiple priors to minimize maximum expected regret, will have different consequences. This exploration of regret-minimizing traders' behavior in k-double auctions illuminates the role of individuals' beliefs in ensuring market outcomes that are consistent with standard economic intuition.

Keywords

• double auctions
• regret minimization
• knightian uncertainty