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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Auctions of Heterogeneous Objects

Simultaneous sealed bid auctions of heterogeneous objects are analyzed. Each bidder's reservation value for an object depends upon the other objects he obtains. Bidders' reservation values are common knowledge. In simultaneous first-price auctions, the set of Walrasian equilibrium allocations contains the set of pure strategy Nash equilibrium allocations which in turn contains the set of strict Walrasian equilibrium allocations. Hence, pure strategy Nash equilibria (when they exist) are efficient. Mixed strategy Nash equilibria may be inefficient. In simultaneous second-price auctions, any efficient allocation can be implemented as a pure strategy Nash equilibrium outcome if a Walrasian equilibrium exists.Journal of Economic LiteratureClassification Numbers: D44, D51.     

Ascending price Vickrey auctions for general valuations

Ascending price auctions involving a single price path and buyers paying their final bid price cannot achieve the Vickrey-Clarke-Groves (VCG) outcome in the combinatorial auctions setting. Using a notion called universal competitive equilibrium prices, shown to be necessary and sufficient to achieve the VCG outcome using ascending price auctions, we define a class of ascending price auctions in which buyers bid on a single price path. Truthful bidding by buyers is an ex post Nash equilibrium in such auctions. By giving discounts to buyers from the final price, the VCG outcome is achieved for general valuations.     

An Asymptotic Solution for Sealed Bid Common-Value Auctions with Bidders Having Asymmetric Information

We investigate a first-price common-value auction where bidders have asymmetric information about an item of unknown value. We compute the unique Nash equilibrium when the bidders are constrained to translation-invariant bid functions. Further, this profile of bid functions is also an asymptotic Nash equilibrium (without the constraint on the bidders' strategies) as the a priori distribution of the true value becomes increasingly diffuse. All bidders have positive expected profits at equilibrium. In the second-price analogue with two bidders there is a continuum of Nash equilibria in which both bidders have positive expected profits. Journal of Economic Literature Classification Number: C7.     

Learning to bid: The design of auctions under uncertainty and adaptation

We examine auction design in a context where symmetrically informed adaptive agents with common valuations learn to bid for a good. Despite the absence of private valuations, asymmetric information, or risk aversion, bidder strategies do not converge to the Bertrand–Nash equilibrium strategies even in the long run. Deviations from equilibrium strategies depend on uncertainty regarding the value of the good, auction structure, the agents? learning model, and the number of bidders. Although individual agents learn Nash bidding strategies in isolation, the learning of each agent, by flattening the best-reply correspondence of other agents, blocks common learning. These negative externalities are more severe in second-price auctions, auctions with many bidders, and auctions where the good has an uncertain value ex post.     

Bid rotation and collusion in repeated auctions

This paper studies bidder collusion with communication in repeated auctions when no side transfer is possible. It presents a simple dynamic bid rotation scheme which coordinates bids based on communication history and enables intertemporal transfer of bidders’ payoffs. The paper derives a sufficient condition for such a dynamic scheme to be an equilibrium and characterizes the equilibrium payoffs in a general environment with affiliated signals and private or interdependent values. With IPV, it is shown that this dynamic scheme yields a strictly higher payoff to the bidders than any static collusion scheme which coordinates bids based only on the current reported signals.     

A Property of Nash Equilibria in Repeated Games with Incomplete Information

We consider two-person non-zero-sum infinitely repeated games with lack of information on one side. The characterization of Nash equilibrium payoffs obtained by Hart allows for complex strategies, which are actually required by some equilibrium payoffs in some games. We show that appropriate one-shot public communication mechanisms make Nash equilibrium payoffs achievable by means of simple strategies. Furthermore, these mechanisms satisfy a notion of self-fulfillment.Journal of Economic LiteratureClassification Numbers: D82, C72.     

Auctions of licences and market structure

Summary. This paper studies sequential auctions of licences to participate in a symmetric market game. Assuming that the rate at which industry profits decrease with repeated entry is not too large, at the unique solution either a single firm preempts entry altogether or entry occurs in every stage, depending on the net benefit of complete preemption to an incumbent. If we relax the assumption, a third outcome can occur: two firms may coordinate their choices to avoid further entry. The analysis employs a new refinement of Nash equilibrium, the concept of recursively undominated equilibrium. Received: February 25, 2000; revised version: September 12, 2000     

Collusion Without Conspiracy: An Experimental Study of One-Sided Auctions

The study investigates collusion-nonfacilitating features of one-sided auctions. We report the results of oral nondescending bid auction experiments in which the strict bid improvement rule was absent, and compare them with the results of sealed bid auction experiments. In the sealed bid experiments the outcomes converged to the competitive equilibrium. In the oral auctions, collusive outcomes emerged and were sustained with bidders using bid matching strategies. We conclude that oral auctions provide opportunities for tacit coordination and collusion enforcement that do not exist under the sealed bid. Therefore, the strict bid improvement rule becomes critical for breaking collusion.     

Individual bidder behavior in first-price private value auctions

Individual bid functions display sensitivity to the strategic considerations inherent in first-price auctions. However, several formal models, including heterogeneous Nash equilibrium bidding models with constant relative risk aversion, perform quite poorly.     

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.     

Compensating for the winner's curse: Experimental evidence

We conduct experiments on common value auctions with rationing. In each auction, the good is randomly allocated to one of the k highest bidders, at the (k+1)st highest price. When k>1, bidders are rationed. As the degree of rationing increases, the equilibrium bid function increases. Consistent with prior literature, we find that bidders suffer from the winner's curse and lose money on average. However, bids in the experiments do adjust in the appropriate direction as the degree of rationing changes, providing support for the comparative statics implications of the theory. Our results are consistent with subjects having an intuitive understanding of the winner's curse, but being unable to compute the equilibrium bid levels.     

Asymmetric auctions with resale: An experimental study

We study auctions with resale based on Hafalir and Krishna's (2008) [6] model. As predicted, weak bidders bid more with resale than without, so that average auction prices tend to increase. When the equilibrium calls for weak types to bid higher than their values with resale they do, but not nearly as much as the theory predicts. In other treatments outcomes are much closer to the risk neutral Nash model's predictions. Bid distributions for weak and strong types are more similar with resale than without, in line with the theory.     

Sealed bid auctions with uncertainty averse bidders

Summary. Traditional analysis of auctions assumes that each bidder's beliefs about opponents' valuations are represented by a probability measure. Motivated by experimental findings such as the Ellsberg Paradox, this paper examines the consequences of relaxing this assumption in the first and second price sealed bid auctions with independent private values. The multiple priors model of Gilboa and Schmeidler [Journal of Mathematical Economics, 18 (1989), 141–153] is adopted specifically to represent the bidders' (and the auctioneer's) preferences. The unique equilibrium bidding strategy in the first price auction is derived. Moreover, under an interesting parametric specialization of the model, it is shown that the first price auction Pareto dominates the second price auction. Received: December 15, 1995; revised version: February 19, 1997     

COMPARING PUBLIC PROCUREMENT AUCTIONS

This article contrasts two auction formats often used in public procurement: first price auctions with ex post screening of bid responsiveness and average bid auctions (ABAs), in which the bidder closest to the average bid wins. The equilibrium analysis reveals that their ranking is ambiguous in terms of revenues, but the ABA is typically less efficient. Using a data set of Italian public procurement auctions run alternately under the two formats, a structural model of bidding is estimated for the subsample of first price auctions and used to quantify the efficiency loss under counterfactual ABAs.     

Equilibrium in Sealed High Bid Auctions

There is a voluminous theoretical literature on sealed high-bid auctions (auctions in which bids are sealed and the high bidder pays his bid). See for example, Vickery (1961), Myerson (1981), riley and Samuelson (1981), Milgrom and Weber (1982), Mathews (1983), Maskin and Riley (1984), Holt(1980) Cox, Smith and Walker (1988). A critical property on which this literature relies is the existence of equilibrium in which buyers' bidding strategies are monotonic in their types. This enables the analyst to perform comparative statics as the distribution of types changes, and to compare the welfare properties of the high-bid auction with those of other auction institutions.     

Learning by trial and error

A person learns by trial and error if he occasionally tries out new strategies, rejecting choices that are erroneous in the sense that they do not lead to higher payoffs. In a game, however, strategies can become erroneous due to a change of behavior by someone else. We introduce a learning rule in which behavior is conditional on whether a player experiences an error of the first or second type. This rule, called interactive trial and error learning, implements Nash equilibrium behavior in any game with generic payoffs and at least one pure Nash equilibrium.     

Rent Seeking with Efforts and Bids

We introduce bids in a rent-seeking contest. Players compete for a prize. Apart from exerting lobbying efforts, they also submit a bid which is payable only if they win the prize. We show that our model has a unique Nash equilibrium in pure strategies, in which each active player submits the same bid, while the sum of all efforts equals that bid. In equilibrium there is underdissipation of rent.     

The symmetric multiple prize all-pay auction with complete information

This paper extends the analysis of the n-player all-pay auction with complete information to cover the case of m≤n prizes, valued in weakly decreasing order, but symmetrically across players. We provide a complete characterization of the Nash equilibrium distributions for this class of auctions and provide an exact expression for the expected revenue generated.     

Undominated Nash Implementation in Bounded Mechanisms

We study implementation in undominated Nash equilibrium by bounded mechanisms. (An undominated Nash equilibrium is a Nash equilibrium in which no agent uses a weakly dominated strategy. A mechanism is bounded if every dominated strategy is dominated by some undominated strategy.) We identify necessary conditions and sufficient conditions for such implementation. These conditions are satisfied in virtually all economic environments, and are also satisfied by interesting correspondences from the social choice literature. For economic settings, we provide a particularly simple implementing mechanism for which the undominated equilibrium outcomes coincide with those obtained from the iterative elimination of weakly dominated strategies. Journal of Economic Literature Classification Numbers: 022, 025, 026.