Level-K Reasoning and Biased Belief Updating in the Dutch Auction with Independent Private Values

In this paper, we propose the models of quantal response equilibrium and level-k reasoning to describe the decision procedure of players in the Dutch auction with independent private values. The estimation results of the models from several different experimental datasets of the Dutch auction disclose learning effects with repeated trials in the Dutch auction, in spite of insignificant difference in bids at the aggregate level across periods. In particular, the bias in belief updating makes players overestimate the winning probability expected at future prices in initial periods but this inclination becomes weaker and even changes to underestimate the expected winning probability in latter periods. Furthermore, we propose a new task that is a simplified version analogous to the decision task of the Dutch auction. We first elicit individual features of the bias in belief updating with this new task, and then, by using the structural model of level-k reasoning, we examine the predictive power of these individual features for the bidding behavior observed in the Dutch auction. We find that it is predictive for the bids in the initial periods of the Dutch auction, but not for the last periods. This result provides a support for the long-standing conjecture in the literature that players are biased in belief updating during the Dutch auction and also confirms the learning effects suggested by the estimation results of the models.