Dan Kovenock

The All-Pay Auction With Complete Information

SummaryIn a (first price) all-pay auction, bidders simultaneously submit bids for an item. All players forfeit their bids, and the high bidder receives the item. This auction is widely used in economics to model rent seeking, R&D races, political contests, and job promotion tournaments. We fully characterize equilibrium for this class of games, and show that the set of equilibria is much larger than has been recognized in the literature. When there are more than two players, for instance, we show that even when the auction is symmetric there exists a continuum of asymmetric equilibria. Moreover, for economically important configurations of valuations, there is no revenue equivalence across the equilibria; asymmetric equilibria imply higher expected revenues than the symmetric equilibrium.

It takes two to tango: Equilibria in a model of sales

We show that the Varian model of sales with more than two firms has two types of equilibria: a unique symmetric equilibrium, and a continuum of asymmetric equilibria. In contrast, the 2-firm game has a unique equilibrium that is symmetric. For the n-firm case the asymmetric equilibria imply mixed strategies that can be ranked by first-order stochastic dominance. This enables one to rule out asymmetric equilibria on economic grounds by constructing a metagame in which both firms and consumers are players. The unique subgame perfect equilibrium of this metagame is symmetric.

The symmetric multiple prize all-pay auction with complete information

Abstract 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.

Asymmetric Information, Information Externalities, and Efficiency: The Case of Oil Exploration

In this article we examine the effect of private information and information externalties on the ex post efficiency of investment in oil exploration. We show that too much drilling tends to occur if firms believe that the area is likely to contain a sizeable pool of oil, and too little drilling occurs if the opposite is true. Bargaining with well-defined property rights to the information externality can eliminate underinvestment, but overinvestment remains a problem because firms have an incentive not to disclose their private information.

A Model of Price Leadership Based on Consumer Loyalty

This paper analyzes a duopolistic price setting game in which firms have loyal consumer segments but cannot distinguish them from price-sensitive consumers. The authors adapt a variant of H. Varians (1980) simultaneous price setting game to analyze price-leader equilibria. The properties of the price-leader equilibria with an exogenously specified leader motivate the construction of a game of timing in which the firm with the larger segment of loyal consumers becomes an endogenous price leader. This demonstrates that consumer loyalty may play an important role in establishing the existence and identity of a price leader. Copyright 1992 by Blackwell Publishing Ltd.

Price leadership in a duopoly with capacity constraints and product differentiation

This paper analyzes Stackelberg price leadership in a duopoly in which firms are capacity constrained and products are imperfect substitutes. Assuming symmetric substitutes, linear demand, and efficient rationing, we characterize the equilibria with an exogenously specified leader. Using the equilibrium profits derived from these games, we argue that over certain ranges of asymmetric capacities an endogenous price leader will emerge. When endogenous leadership does arise, it is the large capacity firm which is the leader. We thus provide a game theoretic model of dominant firm price leadership.

HOW TO SELL A PICKUP TRUCK: "BEAT-OR-PAY" ADVERTISEMENTS AS FACILITATING DEVICES

Abstract This paper examines the profitability of running an advertisement that promises to pay damages to customers who can find a (serious) price offer that the firm will not undercut. We show that such an advertisement can support a collusive price, and furthermore, that no other firm has an incentive to duplicate the advertisement. The results are shown to be relevant in areas that span several topics in the literature, including models of sales, brand loyalty, and the literature on price matching mechanisms.

Contests with Stochastic Abilities

We consider the properties of perfectly discriminating contests in which players’ abilities are stochastic, but become common knowledge before efforts are expended. Players whose expected ability is lower than that of their rivals may still earn a positive expected payoff from participating in the contest, which may explain why they participate. We also show that an increase in the dispersion of a player’s own ability generally benefits this player. It may benefit or harm his rival but cannot benefit the rival more than it benefits himself. We also explore the role of stochastic ability for sequential contests with the same opponent (multibattle contests) and with varying opponents (elimination tournaments) and show that it reduces the strong discouragement effects and holdup problems that may otherwise emerge in such games. High own ability dispersion selects such players into the contest and favors them in elimination contests. (JEL D72, D74)

Extremism Drives Out Moderation

This article examines the impact of the distribution of preferences on equilibrium behavior in conflicts modeled as all-pay auctions with identity-dependent externalities. Centrists and radicals are defined using a willingness-to-pay criterion that admits preferences more general than a simple ordering on the line. Extremism, characterized by a higher per capita expenditure by radicals than centrists, may persist and generate higher aggregate expenditure by radicals, even when they are relatively small in number. Our results demonstrate the importance of the institutions of conflict in determining the role of extremism and moderation in economic, political, and social environments.

Price Leadership and Asymmetric Price Rigidity

Abstract In this paper we present a simple price leadership model in which equilibrium behavior exhibits price rigidity following downward demand shocks and price flexibility after an upturn in demand. The source of this asymmetric rigidity lies in the fact that leader-follower equilibrium prices are lower than their collusive levels and that any firm leading a round of price adjustment must anticipate the optimal price response of the follower. In addition, we find that there is a range of shocks, both positive and negative, in which the identity of the price leader is endogenous; the previous price leader is the only firm that prefers leading a round of price setting to keeping the status quo.