Eliciting Beliefs in Continuous-Choice Games: A Double Auction Experiment

This paper proposes a methodology to implement probabilistic belief elicitation in continuous-choice games. Representing subjective probabilistic beliefs about a continuous variable as a continuous subjective probability distribution, the methodology involves eliciting partial information about the subjective distribution and fitting a parametric distribution on the elicited data. As an illustration, the methodology is applied to a double auction experiment, where traders' beliefs about the bidding choices of other market participants are elicited. Elicited subjective beliefs are found to differ from proxies such as Bayesian Nash Equilibrium (BNE) beliefs and empirical beliefs, both in terms of the forecasts of other traders' bidding choices and in terms of the best-response bidding choices prescribed by beliefs. Elicited subjective beliefs help explain observed bidding choices better than BNE beliefs and empirical beliefs. By extending probabilistic belief elicitation beyond discrete-choice games to continuous-choice games, the proposed methodology enables to investigate the role of beliefs in a wider range of applications.