Knowledge that Transforms

Conventional Bayesian theory of choice under uncertainty, subjective expected utility theory, fails to satisfy the properties of admissibility and existence of well-defined conditional probabilities; weakly dominated acts may be chosen, and the usual definition of conditional probabilities applies only to nonnull events. This paper develops a non-Archimedean variant of subjective expected utility where decisionmakers have lexicographic beliefs. This generalization can be made to satisfy admissibility and yield well-defined conditional probabilities and at the same time allow for "null" events. Copyright 1991 by The Econometric Society.

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-dimen- sional attributes. In addition to the proof of existence, we provide conditions for uniqueness. Our analysis covers location models, the characteristics 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 (Caplin and Nalebuff (1991)) introduces these theorems and develops the application to super-majority voting rules. WE PRESENT A NEW APPROACH to the theory of imperfect competition and apply it to study price competition among differentiated products. The central result is that there exists a pure-strategy price equilibrium for any number of firms producing any set of products. In addition to the proof of existence, we provide conditions for uniqueness. Our model both unites diverse strands of the earlier literature and opens up uncharted areas for future analysis. In particular, we expand the traditional one-dimensional framework to allow for multi-dimen- sional product differentiation. Our approach involves twin restrictions on consumer preferences: one on individuals' preferences, the other on the distribution of preferences across society. These are generalizations of the restrictions supporting 64%-majority rule presented in Caplin and Nalebuff (1988). To prove existence, we apply a new technique of aggregation. This technique is valuable in a variety of other problems. In the companion paper, we use the aggregation result to generalize our earlier work on 64%-majority rule and to characterize the relationship between the distribution of human capital and the distribution of income (Caplin and Nalebuff (1991)). There are additional applications in statistics and in search theory. We begin with a brief review of the early literature on imperfect competition, describing in more detail the existence problem and previous solutions. Section 3 presents our twin assumptions, and shows that they cover many standard cases. In Section 4, we introduce the aggregation theorem and use it in the analysis of demand functions. The proof of existence of equilibrium is in Section

IN THE FIELD OF NONCOOPERATIVE GAME THEORY, Nash equilibrium (Nash (1951)) has played a central role as a solution concept. In bold strokes, one may discern two major interpretations of Nash equilibrium in the context of rational players. The first, which is close to the eductive interpretation of Binmore (1987, 1988) and the complete information interpretation of Kaneko (1987), assumes that the game is played exactly once (if it is a repeated game, the repetition occurs once), and the players have sufficient knowledge and ability to analyze the game in a rational manner. Sometimes it is assumed that all players have consistent hierarchies of beliefs, where the game and their priors are common knowledge. Bayesian interpretation such as proposed by Aumann (1987) advanced this idea to the level that the players have a common prior. From this point of view, however, Nash equilibrium seems far from being satisfactory

When changes in the economic policy regime occur stochastically, asset prices will reflect the possibility of such shifts. In this paper we apply techniques of regulated Brownian motion to obtain closed-form analytic price solutions when policy reaction functions are subject to prospective changes. We focus on the case in which the authorities promise to peg a currency's exchange rate once it reaches a predetermined future level. We also show how an open-ended commitment to exchange-rate targeting may lead to multiple equilibria.

The main result of this paper characterizes voting by committees. There are n voters and K objects. Voters must choose a subset of K. Voting by committees is defined by one monotone family of winning coalitions for each object; an object is chosen if it is supported by one of its winning coalitions. This is proven to be the class of all voting schemes satisfying voter sovereignty and nonmanipulability on the domain of separable preferences. The result is analogous to the characterization of Clarke-Groves schemes in that it exhibits the class of all nonmanipulable schemes on an important domain. Copyright 1991 by The Econometric Society.

Recent work demonstrates that dynastic assumptions guarantee the irrelevance of all redistributional policies, distortionary taxes, and prices-the neutrality of fiscal policy (Ricardian equivalence) is only the "tip of the iceberg." In this paper, we investigate the possibility of reinstating approximate Ricardian equivalence by introducing a small amount of friction in intergenerational links. If Ricardian equivalence depends upon significantly shorter chains of links than do these stronger neutrality results, then friction may dissipate the effects that generate strong neutrality, without significantly affecting the Ricardian result. Although this intuition turns out to be essentially correct, we show that models with small amounts of friction have other untenable implications. We conclude that the theoretical case for Ricardian equivalence remains tenuous.