Carolyn Pitchik

Price competition in a capacity-constrained duopoly

Abstract This paper characterizes the set of Nash equilibria in a model of price-setting duopoly in which each firm has limited capacity, and demand is continuous and decreasing. In general there is a unique equilibrium, so that comparative static exercises are meaningful. The properties of the equilibrium conform with a number of stylized facts. The equilibrium prices are lower, the smaller is demand relative to capacity. When demand is in an intermediate range, the firms use mixed strategies—they randomly hold “sales.” If capacities are chosen simultaneously, before prices, the set of equilibrium capacities coincides with the set of Cournot quantities.

EQUILIBRIUM IN HOTELLING'S MODEL OF SPATIAL COMPETITION

A partly analytical, partly computational approach is used to study mixed strategy equilibria of Hotellings model of sp atial competition in which each of two firms chooses a location in a line segment and a price. There is a unique (up to symmetry) subgame perfect equilibrium in which the locations choices are pure. In it, t he locations are close to the quartiles of the market, and the suppor t of the equilibrium mixed-price strategy of each firm is the union o f two short intervals. There is also a subgame perfect equilibrium in which the firms randomize over locations. Copyright 1987 by The Econometric Society.

Perfect Equilibria in Budget Constrained Sequential Auctions: An Experimental Study

This article presents an experimental study of bidding behavior in sequential auctions in which there are budget constraints and perfect information. Our experiments test both the properties of such auctions and the predictive power of a refinement of the Nash equilibrium concept. We find that budget constraints affect the behavior of bidders and that the trembling-hand perfect equilibrium is generally a good predictor of prices.

Budget-constrained sequential auctions with incomplete information

I study a budget-constrained, private-valuation, sealed-bid sequential auction with two incompletely-informed, risk-neutral bidders in which the valuations and income may be non-monotonic functions of a bidders type. Multiple equilibrium symmetric bidding functions may exist that differ in allocation, efficiency and revenue. The sequence of sale affects the competition for a good and therefore also affects revenue and the prices of each good in a systematic way that depends on the relationship among the valuations and incomes of bidders. The sequence of sale may affect prices and revenue even when the number of bidders is large relative to the number of goods. If a particular good, say α, is allocated to a strong bidder independent of the sequence of sale, then auction revenue and the price of good α are higher when good α is sold first.

The Nature of Equilibrium in a Location Model

Models of location are appropriate in a number of contexts in economics and political science. For example, firms choose where to position stores and which of a spectrum of goods to produce, and politicians select the nature of their platforms. In such models it is natural to look for a collection of locations with the property that the location of each individual is optimal, given the positions of all other individuals. However, the pure strategy Nash equilibrium provides a solution which is both incomplete and unsatisfactory. Incomplete, because in many cases no such equilibrium exists. Unsatisfactory, because even when it does exist it may not be robust to the specification of the model.

Cartels, Profits, and Excess Capacity

A model of a collusive duopoly in which each firm has limited capacity is studied. The negotiated output quotas depend on the bargaining power of the firms, which derives from the damage the firms can do by cutting prices. For fixed capacities, the unit profit of the small firm is at least as large as that of the large firm, and the relative position of the small firm is better when demand is low. When the capacities can be chosen once-and-for-all, there is excess capacity in equilibrium so long as the cost of capacity is not too high. Copyright 1987 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Information Transmission in Regulated Markets

The seminal papers of Vincent P. Crawford and Joel Sobel (1982) and Jerry Green and Nancy Stokey (1980) study models in which a signal about the state of the world is transmitted from a perfectly informed sender to an uninformed receiver. The authors study a model in which multiple signalers compete for consumers. The authors ask how much information is revealed; how consumers shopping around affects this information; and how each is affected by incentives? An implication of the model is that, in a price-regulated market for health care, patients should not be prohibited from gathering more than one opinion.

Profit-Sharing in a Collusive Industry

We study a model in which collusive duopolists divide up the monopoly profit according to their relative bargaining power. We are particularly interested in how the negotiated profit shares depend on the sizes of the firms. If each can produce at the same constant unit cost up to its capacity, we show that the profit per unit of capacity of the small firm is higher than that of the large one. We also study how the ratio of the negotiated profits depends on the size of demand relative to industry capacity, and how this ratio changes with variations in demand.

Equilibria of a two-person non-zerosum noisy game of timing

Necessary and sufficient conditions are obtained for the existence of an equilibrium point (as well as for the existence of a dominating equilibrium point) in a two-person non-zerosum game of timing.

Self-Promoting Investments

When human capital skills differ in their ability to attract offers from alternative employers, a potential inefficiency in human capital investment arises. If a workers output is observed by the labour market only when the worker invests in self-promoting activities, then high-ability workers overinvest in self-promotion. No bond is posted in the contract that both attains efficient investment and minimizes the bond subject to individual rationality constraints and the zero profit condition. The contract is one in which the firm (i) offers to match outside offers strategically and (ii) guarantees a minimum wage. The model predicts that, under both the spot market contract and the efficient contract, wage declines with seniority even when conditioning on high ability. This prediction is consistent with the stylized fact regarding the decline of wages with seniority in academia. The model can also explain how the seniority wage premium may vary across disciplines, time, and schools.