Quantal Response Equilibrium and Overbidding in Private-Value Auctions

Abstract

This paper reports the results of a private-values auction experiment in which expected costs of deviating from the Nash equilibrium bidding function are asymmetric, with the implication that upward deviations will be more likely in one treatment than in the other. Overbidding is observed in both treatments, but is more prevalent in the treatment where the costs of overbidding are lower. We specify and estimate a noisy (quantal response) model of equilibrium behavior. Estimated noise and risk aversion parameters are highly significant and consistent across treatments. The resulting two-parameter model tracks both the average bids and the distribution of bids remarkably well. Alternative explanations of overbidding are also considered. The estimates of parameters from a nonlinear probability weighting function yield a formulation that is essentially equivalent to risk aversion in this context. A model in which players experience a "joy of winning" provides a reasonable fit of the data but does significantly worse than the risk aversion model.

Risk averse behavior in generalized matching pennies games

“…The results of this paper suggest that the quantal response equilibrium may be useful in a wide class of applied econometric studies. With respect to the empirical study of auctions, initial attempts to develop methodologies for doing this in the contexts of both laboratory data (Goeree, Holt, and Palfrey, 2002) and field data (Bajari and Hortacsu, 2001) indicate that this approach is both feasible and promising. (12) CIT (12) CIT (12) CIT (12) CIT (12) CIT ( …”

Introduction to Experimental Game Theory

“…In this model, sophisticated C f subjects have a strong incentive to forego current gains to ''teach'' their possibly adaptive partners to increase effort, but sophisticated C d subjects have no such incentive. 18 This…”

“…FIRST-PRICE SEALED-BID AUCTIONS Goeree, Holt, and Palfrey [18] report experiments that revisit a controversial issue in the experimental auction literature: whether risk aversion can explain the common tendency of human subjects in first-price sealedbid auctions with private values to ''overbid'' relative to the risk-neutral Nash equilibrium. In response to Harrison's [19] ''flat-maximum'' critique of the original overbidding results, Friedman [14] noted that the costs of upward and downward deviations were approximately symmetric, so the weakness of subjects' incentives does not in itself explain overbidding: explaining systematic deviations from equilibrium requires asymmetric costs.…”

Asymmetric information about rivals' types in standard auctions

“…It is an equilibrium behavior for the follower to bid below his valuation with some probability, since the follower earns zero payoff in equilibrium and the leader will not be tempted to deviate as long as the follower puts a sufficient probability mass/density close to his valuation. 10 In Auction 2, if a group leader bids strictly above the follower's valuation (i.e., the latter is not binding), any bid below the follower's valuation can be an equilibrium response. Such a multiplicity should be taken account of in interpreting experimental data.…”

“…First, Bertrand behavior is not subject to bidders' risk attitudes, so the follower's behavior in FPBF and the dependence of a leader's bid on the follower's valuation -coefficients B 2 2 and B 3 2 -are robust to the risk aversion issue. Likewise, the qualitative response by a leader to the rival information, as described in FPBL2 and 10 In fact, given a random tie-breaking rule and a continuous strategy space, any equilibrium response by the follower must involve randomizing below his valuation (See Blume (2003)). Given a discrete strategy space (which is more relevant for our experiment), bidding one's valuation with probability one can be supported as an equilibrium (if the leader bids a unit above it with probability one), but bidding below his valuation can be also supported as an equilibrium.…”