INTEGER PRICING AND BERTRAND-EDGEWORTH OLIGOPOLY WITH STRICTLY CONVEX COSTS: IS IT WORTH MORE THAN A PENNY?

In this paper we analyse the implications of integer pricing for Bertrand Edgeworth oligopoly with strictly convex costs. When price is a continuous variable, there is a generic non-existence of pure-strategy equilibrium. In the case of integer pricing, this is not so. We characterize a set of possible single price equilibria around the competitive price, which if non-empty will constitute the set of single price equilibria if the industry is large enough. Furthermore, we provide an example in which the highest equilibrium price can be arbitrarily far from the competitive price.     

On equilibrium prices in continuous time

State prices are the fundamental building block for dynamic asset pricing models. We provide here a general continuous-time setup that allows to derive non-trivial structural properties for state-prices from economic fundamentals. To this end, we combine general equilibrium theory and théorie générale of stochastic processes to characterize state prices that lead to continuous price systems on the consumption set. We also show that equilibria with such state prices exist.     

Existence and optimality of oligopoly equilibria in linear exchange economies

Summary. We consider a linear exchange economy and its successive replicas. We study the notion of Cournot-Walras equilibrium in which the consumers use the quantities of commodities put on the market as strategic variables. We prove that, generically, if the number of replications is large enough but finite, the competitive behaviour is an oligopoly equilibrium. Then, under a mild condition, which may be interpreted in terms of market regulation and/or market activity, we show that any sequence of oligopoly equilibria of successive replica economies converges to the Walrasian outcome and furthermore that every oligopoly equilibrium of large, but finite, replica is Pareto optimal. Consequently, under the same assumptions on the fundamentals of the economy, one has an asymptotic result on the convergence of oligopoly equilibria to the Walras equilibrium together with a generic existence result for the Cournot-Walras. Received: June 20, 2002; revised version: November 20, 2002 RID="*" ID="*" Part of this paper was written while the second author was visiting the Universidad de Vigo. The support of the department of mathematics is gratefully acknowledged. Correspondence to: J.M. Bonnisseau     

Efficiency in an Economy with Fixed Costs

It is by now well known that in an economy with increasing returns, first-best efficiency may be impossible to attain through an equilibrium concept based on market prices, even if firms are regulated to follow marginal cost pricing. We examine the efficiency issue in a special but important class of economies in which the only source of nonconvexities is the presence of fixed costs. Even in this context, it is possible that none of the equilibria based on marginal cost pricing are efficient (unless additional, strong assumptions are made). We argue that available results on the existence of an efficient two-part tariff equilibrium rely on very strong assumptions, and we provide a positive result using a weak surplus condition. Our approach can also be used to establish the existence of an efficient marginal cost pricing equilibrium with endogenously chosen lump-sum taxes if the initial endowment is efficient in the economy without the production technology.     

Strategic choice of financing systems in regulated and interconnected industries

The growing importance of inter-network exchanges in infrastructure-based utilities influences regulatory choices and access pricing for downstream services using the networks. We analyze this problem in a setting where the infrastructure managers of two bordering countries are in charge of pricing the access to their networks for downstream transport firms that provide international services. Network costs can be financed through public funds and user charges.In this context, access prices are affected by the incomplete internalization of consumers' surplus and infrastructure costs; we analyze how this distortion at the access pricing level generates a distortion in the levels of public funds dedicated to infrastructure financing.Because of these distortions, it turns out that in a non-cooperative setting the second-best outcome might consist in the simultaneous adoption of a no-subsidy system. However, multiple equilibria typically exist and the second-best outcome is never a stable equilibrium. Other properties of the different possible equilibria are studied, as well as the impact of supra-national policies aimed at encouraging the development of international services. Finally, we show that the coordination problems deriving from the existence of multiple equilibria can, sometimes, be solved by separating the choice of a regulatory mode from the access pricing stage, thereby allowing the infrastructure managers to commit to use a specific financing system before setting the access price.     

Economies with Multiple Public Projects

This paper discusses a general equilibrium model of an economy with multiple separately provided public projects. We assume an additively separable cost structure and consider valuation equilibria with separated finance systems, one for each collective good. Under non-Euclidean representation we show the decentralization of Pareto efficient allocations by valuation equilibria and the equivalence of the core and the set of nonnegative valuation equilibria. In the case of Euclidean representation, every Pareto efficient allocation is shown to be supported as an affine valuation equilibrium that is characterized by a personalized price per unit of each public good and a personalized lump sum tax or subsidy. These results complement and clarify already established insights into Lindahl pricing and its generalizations developed in the literature.     

FIRM SIZE AND PRICING POLICY

We relate pricing policy of firms to their size, where firm size is interpreted as the size of the clientele served by the concerned firm. We argue that a firm with a large clientele faces a more severe reputational backlash if it ‘reneges’, i.e., deviates from its earlier price offer. This allows the firm to effectively commit to its offers, leading to a unique equilibrium without delay. Interestingly, this equilibrium corresponds to the equilibrium of the related model that does not allow for reneging possibilities. For smaller firms, however, the reputational effects are much less intense, and consequently the equilibria may involve deviation possibilities. In this case, the equilibria are non‐unique and may involve delays as well.     

Computing equilibria in finance economies with incomplete markets and transaction costs

Summary. Transaction costs on financial markets may have important consequences for volumes of trade, asset pricing, and welfare. This paper introduces an algorithm for the computation of equilibria in the general equilibrium model with incomplete asset markets and transaction costs. We show that economies with transaction costs can be analyzed with differentiable homotopy techniques and thus in the same framework as frictionless economies despite the existence of non-differentiabilities of agents asset demand functions and the existence of locally non-unique equilibria. We introduce an equilibrium selection concept into the computation of economic equilibria that picks out a specific equilibrium in the presence of a continuum of equilibria.Received: 2 December 2002, Revised: 15 November 2004, JEL Classification Numbers: C61, C62, C63, C68, D52, D58, G11, G12. Correspondence to: P. Jean-Jacques HeringsThis research started when Jean-Jacques Herings enjoyed the generous hospitality of the Cowles Foundation for Research in Economics at Yale University. His research has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences and a grant of the Netherlands Organisation for Scientific Research. We thank audiences at Stanford University, UC San Diego, and Venice for discussions on the subject. We are very grateful to an anonymous referee for very helpful comments on an earlier draft.     

Cost Sharing under Increasing Returns: A Comparison of Simple Mechanisms

A technology with decreasing marginal costs is used by agents with equal rights. Each agent demands a quantity of output and costs are divided by means of a fixed formula. Several such mechanisms are compared for the existence of Nash equilibrium demand profiles and for the equity properties of these equilibria. Among three mechanisms, average cost pricing, the Shapley–Shubik cost sharing, and serial cost-sharing, only the latter two possess at least one Nash equilibrium on a reasonable domain of individual preferences. Only the serial cost sharing equilibria pass the equity tests of No Envy and Stand Alone cost.Journal of Economic LiteratureClassification Numbers: C72, D63.     

PLATFORM COMPETITION WITH ENDOGENOUS HOMING

We consider two-sided markets in which consumers and firms endogenously determine whether they single-home, multi-home, or exit the market. We find that the competitive bottleneck allocation in which consumers single-home and firms multi-home is always an equilibrium. In addition, we find equilibria with multi-homing and single-homing on each side of the market. However, unlike the standard pricing result where the side that multi-homes faces higher prices, we find that lower prices coincide with multi-homing: agents find multi-homing more attractive when faced with lower prices. We also show that endogenous homing can induce straddle pricing which deters price undercutting between platforms.     

EXISTENCE AND UNIQUENESS OF AVERAGE COST PRICING EQUILIBRIA: A DEGREE THEORETIC APPROACH

This paper considers the issues of existence and uniqueness of average cost pricing equilibria within the context of a single, regulated, multiproduct monopoly with additively separable costs. We employ basic degree theoretic arguments to establish conditions under which an average cost pricing equilibrium exists. The degree theoretic approach permits the development of uniqueness results in a very natural manner.     

Owner-consumers and efficiency

If each household owns the same fraction of a firm as its share of consumption, shareholders unanimously want marginal-cost pricing. Otherwise, profits are overemphasised relative to consumer surplus.     

Randomized double auctions: gains from trade,trader roles,and price discovery

Experimental double-auction commodity markets are known to exhibit robust convergence to competitive equilibria under stable or cyclical supply and demand conditions, but little is known about their performance in truly random environments. We provide a comprehensive study of double auctions in a stochastic setting where the equilibrium prices, trading volumes and gains from trade are highly variable across periods, and with commodity traders who may buy or sell their goods depending on market conditions and their individual outcomes. We find that performance in this stochastic environment is sensitive to underlying market conditions. Efficiency is higher and convergence to the competitive equilibrium stronger when the potential gains from trade are high and when the equilibrium spans a wide range of quantities, implying a large number of marginal trades. Speculative re-trading is prevalent, especially among those who have little to gain under equilibrium pricing. Those with the largest expected gains typically earn far less than predicted, while those with little or no predicted earnings gain modestly from speculation, leading to some redistribution of gains from high to low expected earners. Excessive trading volumes are associated with negative efficiencies in markets with low gains from trade, but not in the high-gains markets, where zero-sum trading and re-trading appear to enforce efficiency and near-equilibrium pricing. Buyers earn more relative to their competitive equilibrium benchmark than sellers do. Introducing trader specialization leads to fewer trading errors and higher market efficiency, but it does not eliminate zero-sum trading and re-trading.

     

Decentralizing lottery allocations in markets with indivisible commodities

Summary In economies with indivisible commodities, consumers tend to prefer lotteries in commodities. A potential mechanism for satisying these preferences is unrestricted purchasing and selling of lotteries in decentralized markets, as suggested in Prescott and Townsend [Int. Econ. Rev.25, 1–20]. However, this paper shows in several examples that such lottery equilibria do not always exist for economies with finitely many consumers. Other conditions are needed. In the examples, equilibrium and the associated welfare gains are realized if consumptions are bounded or if lotteries are based upon a common sunspot device as defined by Shell [mimeo, 1977] and Cass and Shell [J. Pol. Econ.91, 193–227]. The paper shows that any lottery equilibrium is either a Walrasian equilibrium or a sunspot equilibrium, but there are Walrasian and sunspot equilibria that are not lottery equilibria.This paper is based on Chapter 3 of my doctoral dissertation, written while I was a student at Cornell University. I thank Larry Blume, Yue Yun Chen, David Easley, Aditya Goenka, John Marshall, Bruce Smith, John Wooders and an anonymous referee. I am particularly grateful to Karl Shell and Cheng-Zhong Qin. I thank the Academic Senate at UCSB for financial support.     

The power of ESS: An experimental study

Abstract. Our experimental design mimics a traditional evolutionary game framework where players are matched pairwise to play a symmetric 33 bimatrix game that has two Nash equilibria. One equilibrium is an evolutionary stable state, or ESS; the other is an equilibrium in dominated strategies. Our primary experimental result is the observation that the ESS becomes extremely attractive when subjects have minimal information about the payoff functions, although the dominated equilibrium assures the highest equilibrium payoff. The attractiveness of the ESS is only moderate when players are completely informed about the 33 payoff matrix. Correspondence to: S.K. Berninghaus     

On the Transition from Long-period to Short-period Equilibria

The paper examines the contributions of Myrdal, Lindahl, Hicks and Hayek that initiated the transition from the traditional long-period method to the methods of 'intertemporal' and 'temporary equilibria' in neoclassical general equilibrium analyses. It is shown that in the early contributions the idea of a tendency towards a long-period position was not completely abandoned, and that the new 'dynamic' equilibrium concepts were conceived by some of their originators as useful analytical devices for studying transitions between long-period equilibria only.     

Contests with rank-order spillovers

This paper presents a unified framework for characterizing symmetric equilibrium in simultaneous move, two-player, rank-order contests with complete information, in which each player??s strategy generates direct or indirect affine ??spillover?? effects that depend on the rank-order of her decision variable. These effects arise in natural interpretations of a number of important economic environments, as well as in classic contests adapted to recent experimental and behavioral models where individuals exhibit inequality aversion or regret. We provide the closed-form solution for the symmetric Nash equilibria of this class of games, and show how it can be used to directly solve for equilibrium behavior in auctions, pricing games, tournaments, R&D races, models of litigation, and a host of other contests.     

Equity, Efficiency and Financial Viability: Public-Utility Pricing with Special Reference to Water Supply

The pricing and investment policies of a public enterprise should be designed to achieve efficiency since equity is better pursued by general policy regarding income distribution. Short-run marginal-cost pricing does not generally lead to long-term deficit, but may involve price and surplus/deficit cycles for the case with lumpy investments and growing demand, where the price increases with demand but is reduced with capacity expansion. Taking account of the extra costs of government revenue collection and the likely average price/cost ratio in the economy, the third-best pricing policy is likely to result in long-term surplus, making the objectives of equity, efficiency and financial viability much more consistent with each other than is generally believed. This is particularly true for water with historically increasing costs of additional sources of supply.     

Imperfect Competition in Auction Designs

We study the competition between two owners of identical goods who wish to sell them to a pool of potential buyers. The sellers compete simultaneously setting reserve prices for their second price sealed bid auctions. Upon observing the set reserve prices, the buyers decide simultaneously in which auction to bid. We show that this game has (at least) one equilibrium and that all equilibria are inefficient: reserve prices are not driven to zero (cost). We also discuss where and why the parallel between optimal auction design and optimal pricing in the case of monopoly breaks down for oligopoly.     

On trees and logs

In this paper we contrast the main workhorse model in asset pricing theory, the Lucas (1978) tree model (LT-Model), to a benchmark model in financial equilibrium theory, the real assets model (RA-Model). It is commonly believed that the two models entail similar conclusions since the LT-Model is a special case of the RA-Model. But this is simply wrong: implications of these models can be strikingly at odds. Indeed, under the widely used log-linear specification of households’ preferences, we show that for a large set of initial endowments the LT-Model—even with potentially complete financial markets—admits only peculiar financial equilibria in which the stock market is completely degenerate, in that all stocks offer the same investment opportunity—and yet, allocation is Pareto optimal. We investigate why the LT-Model is so much at variance with the RA-Model, and uncover new results on uniqueness of financial equilibria and introduction of portfolio constraints obtaining in the LT-Model, but not in the RA-Model.