Interdependent Value Auctions with an Insider Bidder

Abstract

(ProQuest: ... denotes formulae omitted.)I. IntroductionMost auction literature assumes that bidders are ex ante homogeneous in terms of the amount of the information they hold about the auctioned object. More specifically, each bidder is assumed to hold a singledimensional information (or signal) about the value of the object. In reality, however, there are many instances in which bidders hold heterogeneous information in terms of its informativeness of the object value. For instance, in a spectrum auction, an incumbent company that has been doing business for a long time should have an advantage in the estimation of the object value compared with newcomers. In addition, in an auction for selling a tract in the outer continental shelf (socalled OCS auction), a company would have an informational advantage over others if it owns and has drilled a neighboring tract.1 The bidders who have superior information as in the above examples can be considered insiders in the auction.The current paper studies the efficiency implication of an insider bidder in standard auctions with two bidders, in which one is an insider and the other is an outsider. Following the standard approach, the value interdependence is modeled by assuming that the two bidders' values are determined by two-dimensional signals. The outsider bidder is only informed of one of the two signals, so he is partially informed of his value. The paper departs from the existing literature by assuming that the insider is fully informed of his value. We ask whether the standard auctions - first-price, second-price, and English auctions - have an efficient equilibrium (i.e., an equilibrium in which the object is allocated to whomever has the higher value).2The two auction formats, first-price and second-price auctions, exhibit a contrasting efficiency performance: the unique undominated Nash equilibrium of the second-price auction yields efficient allocation, whereas the first-price auction does not admit any efficient equilibrium. The difference between the two formats can be explained using the fact that the second-price auction has an ex-post, efficient equilibrium when two bidders exist. The ex-post equilibrium means that neither bidder has an incentive to submit a bid different from the equilibrium bid, even after he learns all the information and precisely knows his value. Consider first the standard setup (Milgrom, and Weber 1982) in which both bidders are outsiders in the sense of holding single-dimensional signals. In this setup, an efficient ex-post equilibrium exists (Maskin 1992). Suppose that one bidder, say bidder 1, has a lower value, so bidder 2 is a winner in the equilibrium. By the property of the ex-post equilibrium, the equilibrium bid of bidder 2 must be higher than the value of bidder 1; otherwise, bidder 1 would have an incentive to deviate and win the object if he precisely knows his value. Consider the case in which bidder 1 becomes an insider and employs the dominant strategy of bidding his value while bidder 2 remains an outsider. Despite this change, bidder 2 has no incentive to revise his bid from the standard case because it is still higher than bidder 1's new bid (which is bidder 1's value and lower than bidder 2's value) and he is paying less than his value and cannot affect the price he pays. By contrast, the first-price auction does not admit any ex-post equilibrium, because a bidder can reduce the price he pays as a winner by decreasing his bid.3 Thus, once a bidder becomes an insider, he will reflect extra information when deciding how much to shade his bid. As a consequence, he may end up bidding a different amount than the outsider who has the same value, which will cause an inefficient allocation.The first-price auction with asymmetric bidders has long been the subject of analysis in the existing literature. Lebrun (1999) has established the uniqueness of the equilibrium. Maskin, and Riley (2000a) have extended the existence to a more general setup. …