Article

# Can Relaxation of Beliefs Rationalize the Winner's Curse?: An Experimental Study

Econometrica (Impact Factor: 3.82). 01/2010; 78(4):1435-1452. DOI: 10.2307/40928444

Source: RePEc

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**ABSTRACT:**Deviations from risk-neutral equilibrium bids in auctions can be related to inconsistent expectations with correct best replies or correct expectations but deviant best replies (e.g. because of risk aversion, regret, quantal-response mistakes). To distinguish between these two explanations, we use a novel experimental procedure and study expectations together with best replies in symmetric and asymmetric auctions. We extensively test the internal validity of this setup. We find that deviations from equilibrium bids do not seem to be because of to wrong expectations but because of deviations from a risk-neutral best reply.The Economic Journal 11/2011; 121(557):1361 - 1397. · 1.95 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**I develop a structural econometric framework for first-price auctions by generalizing the assumption of Bayesian Nash Equilibrium within the context of a level-k behavioral model, which nests equilibrium by allowing bidders to hold heterogeneous beliefs about opponents' bidding strategies. While behavioral heterogeneity causes identification to fail under benchmark equilibrium conditions, independence and exclusion restrictions recover identification of the joint distribution over valuations and bidder-types in heterogeneous populations. Establishing consistent maximum likelihood sieve estimation with an upper semicontinuous population log-likelihood function leads to a natural semi-nonparametric maximum likelihood estimator based on Legendre polynomials. The level-k model introduces a mixture structure to the estimation problem, requiring a generalized expectation maximization algorithm. Presenting evidence from a pilot study of vintage computer auctions, I find a high level of bidder sophistication in the field. To further apply the econometric framework, I characterize expected revenues in first price auctions with level-k bidders, establishing a partial identification result for expected revenues in unidentified models. An empirical analysis of USFS timber auctions finds that a misspecified equilibrium optimal reserve price could reduce expected revenues up to 30% relative to an unbinding reserve price.11/2009; - [Show abstract] [Hide abstract]

**ABSTRACT:**We examine whether the 'Level-k' model of strategic behavior generates re-liable cross-game testable predictions at the level of the individual player. Subjects' ob-served levels are fairly consistent within one family of similar games, but within an-other family of games there is virtually no cross-game correlation. Moreover, the relative ranking of subjects' levels is not consistent within the second family of games. Direct measures of strategic intelligence are generally not correlated with observed levels of reasoning in either family. Our results suggest that the Level-k model is just one of many heuristics that may be triggered in some strategic settings, but not in others.

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