Nonlinear Behavior in Sealed Bid First Price Auctions

Abstract

The extent to which the behavior of people is consistent with game theoretic principles is investigated in a first price sealed bid auction environment Three linear rules of thumb with increasing complexity are used as benchmarks to gauge the accuracy of the Constant Relative Risk Aversion Model (CRRAM). In addition, the CRRAM is tested against the relaxation of the rational expectation hypothesis. Existing competitive bidding experiments cannot clearly distinguish between game theoretic models and linear markdown rules on an individual level. Within the parametric environments studied and reported in the experimental literature, game theoretic solutions are linear over the range of private values in which bid functions are estimated. In this study, agents drew values from non-uniform distributions. As a result, the game theoretic bidding behavior is nonlinear. Due to the nonlinearity, special econometric and numerical techniques are applied to solve the model and obtain the estimates. The CRRAM exhibits good fit of the data. The pseudo R2 is greater than 0.8 in 90 percent of the subjects. The CRRAM is more accurate than the Markdown Model (MM) and the Simple Ad hoc Model (SIMAM) but not as accurate as the Sophisticated Ad hoc Model (SOP AM). The data also supports the relaxation of the rational expectation hypothesis and suggests that substantial increases in the predictive power of game theoretic models can be gained from improvements in the theory of belief formation.