Paul Heidhues

Regular Prices and Sales

We study the properties of a profit-maximizing monopolists optimal price distribution when selling to a loss-averse consumer, where (following Koszegi and Rabin (2006)) we assume that the consumers reference point is her recent rational expectations about the purchase. If it is close to costless for the consumer to observe the realized price of the product, then – in a pattern consistent with several recently documented facts regarding supermarket pricing – the monopolist chooses low and variable “sale” prices with some probability and a high and sticky “regular” price with the complementary probability. Realizing that she will buy at the sale prices and hence that she will purchase with positive probability, the consumer chooses to avoid the painful uncertainty in whether she will get the product by buying also at the regular price. If it is more costly for the consumer to observe the realized price, then – in a pattern consistent with the pricing behavior of some other retailers (e.g. movie theaters) – the monopolist chooses a sticky price and holds no sales. In this case, a sale is less tempting and hence less effective in generating an expectation to purchase with positive probability. We also show that ex-ante competition for loyal consumers leads to sticky pricing while ex-post competition leads to marginal-cost pricing, and discuss several other extensions of the model.

Hiding information in electoral competition

We model a two-candidate electoral competition in which there is uncertainty about a policy-relevant state of the world. The candidates receive private signals about the true state, which are imperfectly correlated. We study whether the candidates are able to credibly communicate their information to voters through their choice of policy platforms. Our results show that the fact that private information is dispersed between the candidates creates a strong incentive for them to bias their messages toward the electorates prior. Information transmission becomes more difficult, the more the information is dispersed between the candidates and the stronger is the electorates prior. Indeed, as more prior information becomes available, welfare can decrease. ZUSAMMENFASSUNG - (Verheimlichen von Informationen im Wahlkampf) In diesem Beitrag wird ein Wahlkampf zwischen zwei Politikern modelliert, in welchem Unsicherheit uber die bessere von zwei Politikalternativen herrscht. Die Kandidaten erhalten private und unvollstandig korrelierte Signale daruber, welche Politik fur die Wahler besser ist. Der Beitrag untersucht, ob die Kandidaten diese Informationen durch die Auswahl ihrer Wahlkampfplattform glaubwurdig an die Wahler weitergeben konnen. Die Tatsache, dass die Kandidaten nicht genau dieselben Information haben, fuhrt dazu, dass sie ihre Informationen teilweise oder vollig ignorieren und ihre Wahlkampfplattform in Richtung der a priori Informationen der Wahler ausrichten. Die Weitergabe der Informationen der Politiker wird umso schwieriger desto mehr die Informationen zwischen den Kandidaten verteilt sind und desto besser die Wahler informiert sind. Im Gleichgewicht kann dies sogar dazu fuhren, dass bessere a priori Informationen der Wahler die Wohlfahrt senken.

All equilibria of the Vickrey auction

Abstract This paper characterizes the set of Nash equilibria in the second-price sealed-bid auction with independent private values and three or more bidders. In addition, we show that any effective reserve price implies uniqueness.

Buyers' Alliances for Bargaining Power

We provide a novel explanation as to why forming an alliance of buyers (or sellers) across separate markets can be advantageous when input prices are determined by bargaining. Our explanation helps to understand the prevalence of buyer cooperatives among small and medium-sized firms.

A group bargaining solution

Abstract We propose a solution for bargaining models where groups of individuals bargain with each other. The solution constitutes a Nash solution within as well as across groups. An individual may be worse off bargaining as a member of a group than bargaining alone (the joint-bargaining paradox) in a pure-bargaining situation. It can be, however, profitable to bargain as a group in a non-pure bargaining situation.

Private Monitoring in Auctions

We study collusion in repeated first-price auctions under the condition of minimal information release by the auctioneer. In each auction a bidder only learns whether or not he won the object. Bidders do not observe other bidders’ bids, who participates or who wins in case they are not the winner. We show that for large enough discount factors collusion can nevertheless be supported in the infinitely repeated game. While there is a unique Nash equilibrium in public strategies, in which bidders bid competitively in every period, there are simple Nash equilibria in private strategies that support bid rotation. Equilibria that either improve on bid rotation or satisfy the requirement of Bayesian perfection, but not both, are only slightly more complex. Our main result is the construction of perfect Bayesian equilibria that improve on bid rotation. These equilibria require complicated inferences off the equilibrium path. A deviator may not know who has observed his deviation and consequently may have an incentive to use strategic experimentation to learn about the bidding behavior of his rivals. ZUSAMMENFASSUNG - (Privates Monitoring in Auktionen) Der Beitrag untersucht, inwieweit Bieter Kollusion, bzw. stillschweigende Abkommen, in wiederholten Erstpreisauktionen aufrecht erhalten konnen, in welchen der Auktionator alle Informationen zuruckhalt. Nach jeder Auktion lernt ein Bieter nur, ob er das Objekt gewonnen hat oder nicht. Ein Bieter kann weder die Gebote der anderen Bieter beobachten, noch kann er beobachten, welche Bieter an der Auktion teilgenommen haben und wer gewonnen hat - solange er nicht selbst das Objekt erhalt. Wir zeigen, dass in dem unendlich wiederholten Spiel fur hinreichend geduldige Bieter Kollusion moglich ist. Es existiert zwar ein eindeutiges Gleichgewicht in offentlichen Strategien, in welchem die Bieter in jeder Periode kompetitiv bieten, aber es gibt einfache Nash-Gleichgewichte in privaten Strategien, die Bieterrotation durchsetzen. Wir zeigen auch, dass Bieterrotation das Ergebnis eines perfekt bayesianischen Gleichgewichtes sein kann. Nash-Gleichgewichte, die hohere erwartete Gewinne als Bieterrotation erzielen, sind nur ein wenig komplexer. Das Hauptergebnis ist die Konstruktion von (essentiell) perfekt bayesianischen Gleichgewichten, welche hohere Gewinne als Bieterrotation erzielen. Nach Abweichungen vom Gleichgewichtspfad, mussen die Bieter in diesen Gleichgewichten komplizierte Ruckschlusse auf das Verhalten Ihrer Wettbewerber ziehen. So weis ein Bieter nach bestimmten Abweichungen nicht, ob diese von seinen Mitspielern beobachtet wurden, und hat ein Interesse daran, durch strategisches experimentieren das Bietverhalten seiner Rivalen kennenzulernen.

FUTILE ATTEMPTS AT SELF-CONTROL

We investigate costly yet futile attempts at self-control when consumption of a harmful product has a binary breakdown/no-breakdown nature and individuals tend to underestimate their need for self-control. Considering time-inconsistent preferences as well as temptation disutility, we show that becoming more sophisticated can decrease welfare and investigate what kind of mistaken beliefs lead to low welfare. With time-inconsistent preferences, being close to perfectly understanding ones preferences but assigning zero probability to true preferences induces the worst outcome. (JEL: D03, D11, D91) (c) 2009 by the European Economic Association.

Modeling Tacit Collusion in Auctions

We study tacit collusion, which we interpret as collusion without communication about strategies, in repeated auctions in which bidders can only observe past winners and not their bids. Strategies cannot discriminate among initially nameless bidders until they have become named through winning an auction. We obtain two classes of results: (1) Completely refraining from using names rules out collusion altogether, and even if naming is permitted, as per our definition of tacit collusion, the lack of communication limits collusive strategies and payoffs among impatient bidders. (2) Sufficiently patient bidders can overcome the attainability constraints imposed by lack of communication and obtain approximately the same collusive gain as absent communication.

Strategic Experimentation with Private Payoffs

We consider a game of strategic experimentation in which players face identical discrete-time bandit problems with a safe and a risky arm. In any period, the risky arm yields either a success or a failure, and the first success reveals the risky arm to dominate the safe one. When payoffs are public information, the ensuing free-rider problem is so severe that equilibrium experimentation ceases at the same threshold belief at which a single agent would stop, even if players can coordinate their actions through mediated communication. When payoffs are private information and the success probability on the risky arm is not too high, however, the socially optimal symmetric experimentation profile can be supported as a perfect Bayesian equilibrium for sufficiently optimistic prior beliefs, even if players can only communicate via binary cheap-talk messages.

All equilibria of the multi-unit Vickrey auction

This paper completely characterizes the set of Nash equilibria of the Vickrey auction for multiple identical units when buyers have non-increasing marginal valuations and there at least three potential buyers. There are two types of equilibria: In the first class of equilibria there are positive bids below the maximum valuation. In this class, above a threshold value all bidders bid truthfully on all units. One of the bidders bids at the threshold for any unit for which his valuation is below the threshold; the other bidders bid zero in this range. In the second class of equilibria there are as many bids at or above the maximum valuation as there are units. The allocation of these bids is arbitrary across bidders. All the remaining bids equal zero. With any positive reserve price equilibrium becomes unique: Bidders bid truthfully on all units for which their valuation exceeds the reserve price.