Risk Attitudes in First-Price Auction Experiments: A Bayesian Analysis - Harrison, Glenn W. (The Review of Economics and Statistics, 1990)
Non-cooperative bidding theory for sealed-bid auctions generally implies testable predictions that are conditioned on the risk attitudes of agents. Received laboratory experiments that purport to test this theory do not generally control for the risk attitudes of subjects. Those experiments exhibit behavior inconsistent with popular bidding models that assume that agents have the same aversion to risk or are all risk neutral. This paper constructs an explicit Bayesian prior distribution for the risk attitudes of experimental subjects and reconsiders the experimental results. It finds that observed bidding behavior is still inconsistent with the Nash predictions when explicit prior weights are attached to alternative assumptions about subject risk attitudes. Thus one cannot account for observed bidding anomalies by appealing to uncontrolled nuisance variables such as risk attitudes. Non-cooperative bidding theory for sealed-bid auctions generally implies testable predictions that are conditioned on the risk attitudes of agents. Archetypical of this result is the Nash Equilibrium prediction for First Price auctions for an object that is valued by agents in an independent and private manner. Received laboratory experiments that purport to test this theory do not generally control for the risk attitudes of subjects. Those experiments exhibit behavior inconsistent with popular bidding models that assume that agents have the same aversion to riskor are all risk neutral. In this paper we construct an explicit prior distrlbution for the risk attitudes of experimental subjects and reconsider the experimental results. We find that observed bidding behavior is indeed consistent with the Nash predictions when explicit prior weights are attached to alternative assumptions about subject risk aversion. However, when one allows for risk loving subjects as well, observed behavior is inconsistent with Nash predictions. Thus one cannot account for observed bidding anomalies by appealing to uncontrolled nuisance variables such as risk attitudes. In section I we consider a specific Nash Equilibrium (NE) bidding model due to Cox, Roberson and Smith (1982) and Cox, Smith and Walker (1988) that clearly illustrates the risk-sensitivity of the theoretical predictions. In section II we provide independent evidence of the risk attitudes of experimental subjects in a test for risk attitudes developed by Harrison (1986a). This evidence allows us to construct an explicit prior probability density function over the coefficient of (constant relative) risk attitudes employed in the specific bidding model of section I. In section III we reconsider the evidence from the First Price (FP) experiments reported in Cox, Roberson and Smith (1982) and Cox, Smith and Walker (1983a, 1983b). I. A Specific Bidding Model Cox, Roberson and Smith (1982), hereafter CRS, present a model based on a power function utility specification for agent i: Ui(y) y= (1) Received for publication August 31, 1987. Revision accepted for publication December 18, 1989. * University of South Carolina. I am grateful to two anonymous referees for helpful comments, although they are not responsible for my conclusions.