Barry Nalebuff

Prices and Incentives: Towards a General Theory of Compensation and Competition

This article analyzes the role of competitive compensation schemes (in which pay depends on relative performance) in economies and imperfect information. These compensation schemes have desirable risk, incentive, and flexibility properties; they provide for an automatic adjustment of rewards and incentives in response to common changes in the environment. When environmental uncertainty is large, such schemes are shown to be preferable to individualistic reward structures; in the limit, as the number of contestants becomes large, expected utility may approach the first-best (perfect information) level. We study the design of contests, including the optimal use of prizes versus punishments and absolute versus relative performance standards. The analysis can also be viewed as a contribution to the multiagent, single-principal problem.

AGGREGATION AND IMPERFECT COMPETITION: ON THE EXISTENCE OF EQUILIBRIUM

We present a new approach to the theory of imperfect competition and apply it to study price competition among differentiated products. The central result provides general conditions under which there exists a pure strategy price equilibrium for any number of firms producing any set of products. This includes products with multi-dimensional attributes. In addition to the proof of existence, we provide conditions for uniqueness. Our analysis covers location models, the characteristic approach, and probabilistic choice together in a unified framework. To prove existence, we employ aggregation theorems due to Prekopa (1971) and Borell (1975). Our companion paper [CFDP 938] introduces these theorems and develops the application to super-majority voting rules.

Bundling as an Entry Barrier

In this paper we look at the case for bundHng in an oHgopohstic environment. We show that bundhng is a particularly effective entry-deterrent strategy. A company that has market power in two goods, A and B, can, by bundling them together, make it harder for a rival with only one of these goods to enter the market. Bundling allows an incumbent to credibly defend both products without having to price low in each. The traditional explanation for bundling that economists have given is that it serves as an effective tool of price discrimination by a monopolist. Although price discrimination provides a reason to bundle, the gains are small compared with the gains from the entry-deterrent effect.

Dragon-slaying and ballroom dancing: The private supply of a public good

Many public goods typically are supplied by the efforts of a single individual. A purely selfinterested agent could provide a public good if his own participation in the benefits justifies his cost. In this paper we model the decision of how a private individual decides when to take the initiative and pay for the provision of a public good. As an application of the optimal auctions literature to the public goods problem, the emphasis is placed on the effect of additional agents on potential supply. The free rider problem is shown to be less important as the population size of potential volunteers increases; we demonstrate conditions in which the first best is attained in the limit as the population size approaches infinity.

Credible Pretrial Negotiation

Pretrial negotiation is a structured environment in which to study bargaining with incomplete information. When a plaintiff believes that a defendant owes him damages, he may first attempt to reach a private settlement before resorting to a costly court-imposed judgment. A central issue in their negotiations is whether the plaintiffs threat to litigate is credible. It is possible for the plaintiff to undermine the credibility of his litigation threat by making a settlement demand that is insufficient. As a result, the plaintiff must raise his settlement demand to limit the amount of bad news he can learn if his offer is rejected. When this credibility constraint is binding, traditional comparative static results are reversed. In addition, even though the defendant is being sued, he wants the plaintiffs threat to be credible.

Aggregation and Social Choice: A Mean Voter Theorem

A celebrated result of Black (1984a) demonstrates the existence of a simple majority winner when preferences are single-peaked. The social choice follows the preferences of the median voters most preferred outcome beats any alternative. However, this conclusion does not extend to elections in which candidates differ in more than one dimension. This paper provides a multi-dimensional analog of the median voter result. We show that the mean voters most preferred outcome is unbeatable according to a 64%-majority rule. The weaker conditions supporting this result represent a significant generalization of Caplin and Nalebuff (1988). The proof of our mean voter result uses a mathematical aggregation theorem due to Prekopa (1971, 1973) and Borell (1975). This theorem has broad applications in economics. An application to the distribution of income is described at the end of this paper; results on imperfect competition are presented in the companion paper [CFDP 937].

The Devolution of Declining Industries

In declining industries capacity must be reduced in order to restore profitability. Who bears this burden? Where production is all or nothing, there is a unique subgame-perfect equilibrium: the largest firms exit first [Ghemawat and Nalebuff, 1985]. In this paper firms continuously adjust capacity. Again, there is a unique subgame-perfect equilibrium. All else equal, large firms reduce capacity first, and continue to do so until they shrink to the size of their formerly smaller rivals. Intuitively, bigger firms have lower marginal revenue and correspondingly greater incentives to reduce capacity. This prediction is supported by empirical findings.

On 64%-Majority Rule

Many electoral rules require a super-majority vote to change the status quo. Without some restriction on preferences, super-majority rules have paradoxical properties. For example, electoral cycles are possible with anything other than 100 percent majority rule. The auth ors show that these problems do not arise if there is sufficient simi larity of attitudes among the voting population. Their definition of social consensus involves two restrictions on domain: one on individu al preferences, the other on the distribution of preferences. When th is consensus exists, 64 percent majority rule has many desirable prop erties, including the elimination of all electoral cycles. Copyright 1988 by The Econometric Society.

Competing Against Bundles

In this paper, we show that a firm that sells a bundle of complementary products will have a substantial advantage over rivals who sell the component products individually. Furthermore, this advantage increases with the size of the bundle. Once there are four or more items, the bundle seller does better than when it sells each component individually. This model helps explain one factor in how Microsoft achieved dominance in the Office software suite against pre-existing and well-established rivals in each component. This paper is a sequel to Bundling [Nalebuff (1999) http://papers.ssrn.com/sol3/papers.cfm?abstract_id=185193].

Asymmetric equilibria in the war of attrition

In Maynard Smiths seminal analysis of the war of attrition the gains to competition are assumed to be public knowledge. As a result, the evolutionary equilibrium is a mixed strategy. More recent work has emphasized the role of private information (degree of hunger etc.) in generating an evolutionary equilibrium in pure strategies, under the assumption that competitors are observationally identical. In this paper it is shown that, for the war of attrition with private information, there is, in general, a continuum of asymmetric equilibria. Thus, even with only a payoff-irrelevant observational difference between potential competitors, very asymmetric behavior is evolutionally viable.