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Top1. Introduction
In this paper I propose a model of reference dependent preferences to explain overbidding in first- and second-price private and common value auctions. Bidders compute gains and losses relative to a reference point, which is assumed to be proportional to the value of the object. I derive symmetric equilibrium bid strategies in all four cases and test the model empirically against other alternatives using data from previous well-known experiments. Like Stigler (1950) I believe that theories should be evaluated according to (i) generality, (ii) tractability and (iii) congruence with reality. The model I present in this paper is general (standard preferences being a special case), tractable (it is straightforward to generalize known symmetric equilibrium bid functions to include reference dependence) and fits experimental data better than models with standard (risk neutral) preferences and other alternatives.
It is a well-established and robust empirical fact that experimental subjects overbid relative to the Risk Neutral Nash Equilibrium (RNNE) strategy in several classes of auctions. Kagel and Roth (1995) provides a good survey of the literature and experimental results. Overbidding relative to the RNNE can be rationalized by considering preferences differing from standard risk neutrality such as risk aversion, joy of winning as in Cox et al. (1988) and spite motives as in Morgan et al. (2003) or through bounded rationality.
In independent private value (IPV) first-price auctions the generally accepted explanation for overbidding is risk aversion. However, other possibilities have been explored, like Goeree et al. (2002) who use non-linear probability weighting plus Quantal Response Equilibrium to describe choices in a discrete first-price private value auction. Overbidding has also been observed in IPV second-price auctions, Cooper and Fang (2008) carried out a series of experiments where bidders could buy noisy signals about the value of the opponents. Their results provide support for both bounded rationality and non-standard preferences as causes of overbidding.
Overbidding in common value actions is often attributed to the tendency of subjects to overestimate the value of the object. This intuition has been analyzed by Eyster and Rabin (2005), who introduced the Cursed Equilibrium concept where bidders do not fully take into account the informational content of winning and as a consequence misestimate the true value of the object. Later, Crawford and Iriberri (2007a) proposed a non-equilibrium model to explain overbidding using the Level-k model of Nagel (1995) and Stahl and Wilson (1995), where bidders have different depths of reasoning and best respond given their inconsistent beliefs. Bounded rationality certainly plays a role in this tendency of subjects to overbid, however, some researchers such as Ivanov et al. (2010) provide evidence that factors other than inconsistent beliefs might be at work in explaining overbidding in common-value auctions.
All of the previous explanations have the characteristic of being applicable to some type of auctions but not others. For example, risk aversion can explain overbidding in IPV first-price auctions but not in second-price since the weakly dominant strategy of bidding the value is independent of risk attitudes. Moreover, we share with other researchers our reservations as to the role played by risk aversion as the cause of overbidding. Kagel and Roth (1992) claim that “risk aversion cannot be the only factor and may well not be the most important factor behind bidding above the risk neutral Nash Equilibrium found so often in first-price private value auctions.” Goeree et al. (2002) observe “In spite of the obvious appeal of risk aversion as an explanation, we too are not completely convinced that it is the best explanation.”