Bid shading

In an auction, bid shading describes the practice of a bidder placing a bid that is below what they believe a good is worth.

Bid shading is used for one of two purposes. In a common value auction with incomplete information, bid shading is used to compensate for the winner's curse. In such auctions, the good is worth the same amount to all bidders, but bidders don't know the value of the good and must independently estimate it. Since all bidders value the good equally, the winner will generally be the bidder whose estimate of the value is largest. But if we assume that in general bidders estimate the value accurately, then the highest bidder has overestimated the good's value and will end up paying more than it is worth. In other words, winning the auction carries bad news about a bidder's value estimate. A savvy bidder will anticipate this, and reduce their bid accordingly.

Bid shading is also used in First-price Auctions, where the winning bidder pays the amount of his bid. If a participant bids an amount equal to their value for the good, they would gain nothing by winning the auction, since they are indifferent between the money and the good. Bidders will optimize their expected value by accepting a lower chance of winning in return for a higher payoff if they win.

In a first-price common value auction, a savvy bidder should shade for both of the above purposes.

Bid shading is not only a normative theoretical construct, it was detected in the above-mentioned real world auction markets (Jofre-Bonet and Pesendorfer 2003, Zeithammer 2006). Previous theoretical work on sequential auctions focused either on bid shading in an exogenous sequence of auctions (see, for example, Milgrom and Weber 2000, Jeitschko 1999), or on strategic auctioning to short-lived buyers, who never want to shade their bids (see, for example, Vulcano et al. 2002). This paper provides the ﬁrst model of a sequential auction with both endogenous strategic selling and forward-looking longer-lived buyers who can shade their bids. The model’s contribution is the analysis of the best response of the seller to strategic bid shading, and the exposition of a market equilibrium, in which bidders do not always shade. The most related model of bidding is Jeitschko (1999), who ﬁnds that relatively to exogenous and certain future supply, exogenous but uncertain future supply leads to a proportional bid increase. In contrast, high-valuation bidders shade more than low valuation bidders here. The most related model of optimal sequential auctioning by Vulcano, van Ryzin, and Maglaras (2002) (VRM), who study a monopolist selling to unit-demand strategic buyers who each only lives for one period. While VRM’s bidders do not shade their bids by assumption, strategic sequential auctioning has an effect on their bidding strategy because they are forward-looking: there is an incentive to overbid and make the seller sell more units in the current period than would be optimal for her.

Topics in game theory

Definitions	Normal-form game Extensive-form game Escalation of commitment Graphical game Cooperative game Succinct game Information set Hierarchy of beliefs Preference

Equilibrium concepts	Nash equilibrium Subgame perfection Mertens-stable equilibrium Bayesian Nash equilibrium Perfect Bayesian equilibrium Trembling hand Proper equilibrium Epsilon-equilibrium Correlated equilibrium Sequential equilibrium Quasi-perfect equilibrium Evolutionarily stable strategy Risk dominance Core Shapley value Pareto efficiency Gibbs equilibrium Quantal response equilibrium Self-confirming equilibrium Strong Nash equilibrium Markov perfect equilibrium

Strategies	Dominant strategies Pure strategy Mixed strategy Tit for tat Grim trigger Collusion Backward induction Forward induction Markov strategy

Classes of games	Symmetric game Perfect information Simultaneous game Sequential game Repeated game Signaling game Screening game Cheap talk Zero-sum game Mechanism design Bargaining problem Stochastic game n-player game Large Poisson game Nontransitive game Global games Strictly determined game Potential game

Games	Prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock-paper-scissors Pirate game Dictator game Public goods game Blotto games War of attrition El Farol Bar problem Fair division Fair cake-cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Prisoners and hats puzzle Trust game Princess and monster game Monty Hall problem Rendezvous problem

Theorems	Minimax theorem Nash's theorem Purification theorem Folk theorem Revelation principle Arrow's impossibility theorem

Key figures	Albert W. Tucker Amos Tversky Ariel Rubinstein Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin Jean Tirole Jean-François Mertens John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Thomas Schelling William Vickrey

See also	All-pay auction Alpha–beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition List of game theorists List of games in game theory No-win situation Topological game Tragedy of the commons Tyranny of small decisions

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Bid shading

See also