Quantal Response Equilibrium and Overbidding in Private-Value Auctions

This paper applies the quantal response equilibrium (QRE) model to study overbidding in private-values auctions. Experimental evidence shows that the prevalence of overbidding depends on the cost of overbidding relative to underbidding, as predicted theoretically. We use QRE as an error structure to estimate parameters of several competing models of overbidding. A QRE model based on risk averse bidders closely tracks the exact distribution of bids. The estimated parameters are significant and consistent across treatments. Journal of Economic Literature Classification Numbers: C72, C92, D44.     

Bidding in private-value auctions with uncertain values

Auctions are often used to sell idiosyncratic goods difficult for potential bidders to value ex ante. Laboratory auctions with uncertainty over final values in this experiment resulted in 18% and 27% of bids above the expected value of the item in private-value first-price and English auctions, respectively. Risk-seeking preferences as measured on an individual decision task cannot explain overbidding and the first-price auction results suggest that risk aversion may not be a good explanation for bidding behavior observed with certain values. Several candidate explanations fail to explain overbidding, rather it appears to stem from some bidders who are prone to overbidding. Relative to first-price auctions, the size and frequency of overbids are significantly larger in English auctions, while more English auctions are won by overbidders. Differences between the formats appear to be driven by the dynamic nature of English auctions which is consistent with popular notions of “auction fever.”     

Optimistic irrationality and overbidding in private value auctions

Bidding one’s value in a second-price, private-value auction is a weakly dominant solution (Vickrey in J Finance 16(1):8–37, 1961), but repeated experimental studies find more overbidding than underbidding. We propose a model of optimistically irrational bidders who understand that there are possible gains and losses associated with higher bids but who may overestimate the additional probability of winning and/or underestimate the potential losses when bidding above value. These bidders may fail to discover the dominant strategy—despite the fact that the dominant strategy only requires rationality from bidders—but respond in a common sense way to out-of-equilibrium outcomes. By varying the monetary consequences of losing money in experimental auctions we observe more overbidding when the cost to losing money is low, and less overbidding when the cost is high. Our findings lend themselves to models in which less than fully rational bidders respond systematically to out-of-equilibrium incentives, and we find that our model better fits the effects of our manipulations than most of the existing models we consider.     

Experimental tests of Tullock’s contest with and without winner refunds

We examined experimentally the two-agent, complete-information Tullock’s contest, with and without refund for the winner. We find that the average bids in the refund group are higher than the average bids in the group without a refund, consistent with the theory. However, the auctioneer does not increase his profit if he changes the design of the contest by reimbursing the winner’s cost of effort. We also find underbidding for the low-valuation players and overbidding for the high-valuation player in a contest with a refund. Some players chose the corner solution of staying out of the game by biding zero.     

Individual behavior of first-price auctions: The importance of information feedback in computerized experimental markets

This article reports the results of an individual choice experiment designed to test the Nash equilibrium predictions of the first-price sealed-bid auction. A subject faced in 100 auctions always the same resale value and competed with computer-simulated bids. The design used between-subjects variation and involved information feedback as the treatment variable. Earlier experimental work on first price auctions has frequently reported an overbidding relative to the risk neutral Nash equilibrium. Our data provide evidence that overbidding can be fostered by the standard information feedback in auction experiments, which, after each auction, reveals the winning bid only. By means of learning direction theory we explain the individual bidding dynamics in our experiment. Finally we apply impulse balance theory and make long run predictions of individual bidding behavior.     

EXPERIMENTAL EVIDENCE ON ENGLISH AUCTIONS: ORAL OUTCRY VERSUS CLOCK

This paper tests experimentally, in a common value setting, the equivalence between the Japanese English auction (or clock auction) and an oral outcry auction where bidders are allowed to call their own bids. We find that (i) bidding behaviour is different in each type of auction, but also that (ii) this difference in bidding behaviour does not affect significantly the auction prices. This lends some support to the equivalence between these two types of auction. The winner's curse is present: overbidding led to higher than expected prices (under Nash bidding strategies) in both types of auction. Although interesting and encouraging, the results clearly indicate that further research is necessary, particularly with a modified experimental design.     

Overbidding in fixed rate tenders—an empirical assessment of alternative explanations

This paper investigates various theories explaining banks’ overbidding in the fixed rate tenders of the European Central Bank (ECB). Using auction data from both the Bundesbank and the ECB, we show that none of the theories can on its own explain the observed overbidding. This implies that the proposed new rules by the ECB, aimed at neutralizing interest rate expectations, would not eliminate overbidding if the rationing rule in the fixed rate tenders remains unchanged.     

Endowment effects in contests

We experimentally study overbidding in contests and find that overbidding is significantly higher when subjects are given a large per-experiment endowment rather than when the endowment is given per-period. Risk-aversion and non-monetary utility of winning can partially explain our findings.     

SUBJECTIVE PROBABILITIES IN GAMES: AN APPLICATION TO THE OVERBIDDING PUZZLE*

This article illustrates how the joint elicitation of subjective probabilities and preferences may help us understand behavior in games. We conduct an experiment to test whether biased probabilistic beliefs may explain overbidding in first‐price auctions. The experimental outcomes indicate that subjects underestimate their probability of winning the auction, and indeed overbid. When provided with feedback on the precision of their predictions, subjects learn to make better predictions, and to curb significantly overbidding. The structural estimation of different behavioral models suggests that biased probabilistic beliefs are a driving force behind overbidding, and that risk aversion plays a lesser role than previously believed.     

Costless discrimination and unequal achievements in an experimental tournament

We investigate the emergence of discrimination in an experiment where individuals affiliated to different groups compete for a monetary prize, submitting independent bids to an auctioneer. The auctioneer receives perfect information about the bids (there is no statistical discrimination), and she has no monetary incentive to favor the members of her own group (the bidders are symmetric). We observe nonetheless some discrimination by auctioneers, who tend to assign the prize more frequently to a member of their own group when two or more players put forward the highest bid. Out-group bidders react to this bias and reduce significantly their bids, causing an average decay of their earnings throughout the game, with cumulative effects that generate unequal outcomes. Because the initial bias is costless, such mechanism can survive even in a competitive market, providing a rationale for the long-run persistence of discrimination.     

The Repo Auctions of the European Central Bank and the Vanishing Quota Puzzle*

Until June 2000 the European Central Bank (ECB) used fixed rate tenders for its weekly repo auctions. A switch to variable rate tenders became necessary due to massive overbidding by banks. In this paper we introduce a stylized game among banks to investigate this overbidding phenomenon. Our results confirm the weakness of the fixed rate tender format and indicate that the ECB's liquidity management has significantly improved since the switch to the variable rate system. Yet recent episodes of rate cut expectations suggest that the ECB's practice of setting a minimum bid rate should be abandoned in favor of a more symmetric interest rate target.     

Bidding ‘as if’ risk neutral in experimental first price auctions without information feedback

Experimental research on first price sealed bid auctions has usually involved repeated settings with information feedback on winning bids and payoffs after each auction round. Relative to the risk neutral Nash equilibrium, significantly higher bidding has been reported. The present paper reports the results of experimental first price auctions with n=7 where feedback on payoffs and winning bids is withheld. Under these conditions, average bidding is below the risk neutral Nash equilibrium prediction but converges to it with repetition.

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Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.      

The preference reversal phenomenon: Response mode,markets and incentives

Summary This paper addresses the apparent conflict between the results of experiments on individual choice and judgement and the results of market experiments. Data are reported for experiments designed to analyze the effects of (a) economic incentives, repetition, feedback and information and (b) choice and valuation response modes on (c) subjects' decisions in paired market and nonmarket environments. Causes of divergent market and nonmarket behavior are identified in the context of the preference reversal phenomenon (PRP). Study of the PRP is extended to two types of market environments. The PRP is observed on the first repetition in a market setting (second price auction) with immediate feedback, both with and without financial incentives. However, after five repetitions of the auction, the subjects' bids are generally consistent with their choices and the asymmetry between the rates of predicted and unpredicted reversals disappears. An individual pricing task using the BDM mechanism yields similar results on the first repetition but results which differ from the second price auction on the fifth repetition. Choice tasks produce lower rates of reversals than do pricing tasks in both market and individual decision making settings.We are grateful for financial support from the National Science Foundation (grant no. SES-8820552) and the California Institute of Technology. Research facilities were provided by the Economic Science Laboratory at the University of Arizona. Valuable computer programming was provided by Sean Coates and Shawn LaMaster. We thank Professor Jeffrey Dubin for his help in setting up the software for the generalized Tobit model, and Professors Joyce Berg, Graham Loomes, and Charles R. Plott for helpful comments.     

Dominant Strategy Adoption and Bidders' Experience with Pricing Rules

Truthful revelation is a dominant strategy in both English (oral ascending bid) and second-price sealed-bid private-values auctions. Controlled observations of English auctions are largely consistent with the dominant strategy prediction, but laboratory second-price auctions exhibit substantial and persistent overbidding, even with prior experience. However, the experience of having bid in an English auction has a significant learning effect, moving bidding in subsequent second-price auctions closer to the dominant strategy. I explore two treatments isolating facets of the lessons learned from English auction participation, leading me to the following conclusions. Part of the lesson carried over appears to be considering prices one-by-one, but most of it appears to be a crude awareness that overbidding leads to losses. A claim that English auction experience teaches subjects to recognize the dominant strategy in second-price auctions seems overly optimistic. I introduce a nonparametric technique to test coefficient restrictions when the assumption of normally distributed errors is untenable.     

Market experience eliminates some anomalies—and creates new ones

We report two experiments which investigate whether experience of decision making in repeated markets purges behaviour of preference reversals. We investigate two behavioural mechanisms that may be shaping bids in repeated auctions: A tendency to adjust bids towards previously observed market prices, and a tendency to reduce bids following bad market outcomes. We find little support for the former but strong support for the latter. Also, whilst ‘just enough’ market exposure eliminates the typical preference reversal phenomenon, continued exposure fosters the mirror image anomaly. Therefore, although market experience shapes behaviour, in our experiments, it does not generally promote consistency with standard preference theory.     

Testing the continuity of individual bid density functions: Some further results

This brief paper analyzes the bidding behavior in OCS oil auctions of six individual bidders (using solo bids only) and of a consortium bidder over the period 1963–1979. Included are bidders that bid over the entire period, one that bids for only a short time at the beginning, and one that first makes such bids in 1970. Our findings strongly support those reported in an earlier paper for five bidders and a brief, three-auction sample period: bidders commonly utilize multiple bids of single dollar values within a given auction. The strength of the present results – for three of the seven bidders, over 30% of the bids made fell into this category – further buttresses our conjecture that the use of continuous bid functions is inappropriate for modelling offshore oil lease auctions.     

Auctions with Anticipated Emotions: Overbidding,Underbidding, and Optimal Reserve Prices*

The experimental literature has documented that there is overbidding in second‐price auctions, regardless of the valuations of bidders. In contrast, in first‐price auctions, there tends to be overbidding for large valuations, but underbidding for small valuations. We show that the experimental evidence can be rationalized by a simple extension of the standard auction model, where bidders anticipate (constant) positive or negative emotions caused by the mere fact of winning or losing. Even if the emotional (dis‐)utilities are very small, the revenue‐maximizing reserve price might be significantly different from the standard model. Moreover, decreases with the number of bidders.     

Hybrid allocation mechanisms for publicly provided goods

Motivated by efficiency and equity concerns, public resource managers have increasingly utilized hybrid allocation mechanisms that combine features of commonly used price (e.g., auction) and non-price (e.g., lottery) mechanisms. This study serves as an initial investigation of these hybrid mechanisms, exploring theoretically and experimentally how the opportunity to obtain a homogeneous good in a subsequent lottery affects Nash equilibrium bids in discriminative and uniform price auctions. The lottery imposes an opportunity cost to winning the auction, systematically reducing equilibrium auction bids. In contrast to the uniform price auction, equilibrium bids in the uniform price hybrid mechanism vary with bidder risk preferences. Experimental evidence suggests that the presence of the lottery and risk attitudes (elicited through a preceding experiment) impact auction bids in the directions predicted by theory. Finally, we find that theoretically and experimentally, the subsequent lottery does not compromise the efficiency of the auction component of the hybrid mechanisms.     

Limited Consumer Attention in International Trade

This paper introduces a model of limited consumer attention into an otherwise standard new trade theory model with love‐of‐variety preferences and heterogeneous firms. In this setting, we show that international integration needs not be welfare enhancing if the consumers' capacity to gather and process information is limited. Rather, it intensifies competition for scarce consumer attention, which causes mutual overbidding of producers in their advertising expenditures. The mutual overbidding renders advertising—which is informative in principle—wasteful and diverts purchases to imported goods at an inefficient scale. Wasteful advertising provides scope for policy intervention in the form of an advertising tax. However, if the tax instrument is not allowed to discriminate against foreign producers, it cannot eliminate inefficient diversion of consumer purchases to imports; hence it needs not be successful in securing gains from international integration in this framework.     

Laboratory Testbeds and Non-Market Valuation: The Case of Bidding Behavior in a Second-Price Auction with an Outside Option

Researchers now use the lab to examine the behavioral underpinnings of valuation before the field application which some argue has less experimental control. But lab valuation work raises its own set of concerns when it uses private goods to explore non-market valuation behavior because private goods have substitutes often unaccounted for in the lab. Therefore, the lab as a tool to testbed field valuation work may be limited. Herein we design an induced valuation experiment to explore bidding behavior in a second-price auction with an outside option that is a perfect substitute for the auction commodity. Theory predicts that rational bidders will consider the prices of outside options when formulating bidding strategies, and will reduce their bids whenever their resale value exceeds the price of the outside option. Our results suggest that bidders account for outside options when formulating bids with behavior following comparative static predictions. In addition, we provide evidence concerning hypothetical versus actual behavior with induced values – the data suggesting a hypothetical bias in the level of bids but not in bid shaving.