Martin J. Osborne

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.

Spatial Models of Political Competition under Plurality Rule: A Survey of Some Explanations of the Number of Candidates and the Positions They Take

This paper surveys work that uses spatial models of political competition to explain the number of candidates and the positions that they take in plurality rule elections.

Noncooperative models of bargaining

Publisher Summary This chapter focuses on the noncooperative models of bargaining. John Nashs (1950) path- breaking paper introduces the bargaining problem, and his pioneering work on noncooperative bargaining theory was taken up again and developed by numerous authors. The target of such a noncooperative theory of bargaining is to find theoretical predictions of what agreement, if any, will be reached by the bargainers, thereby to explain the manner in which the bargaining outcome depends on the parameters of the bargaining problem and to shed light on the meaning of some of the verbal concepts that are used when bargaining is discussed in ordinary language. Three directions in which progress has been particularly fruitful are (1) sequential models have been introduced in studying specific bargaining procedures, (2) refinements of Nash equilibrium have been applied, and (3) bargaining models have been embedded in market situations to provide insights into markets with decentralized trading. In spite of this progress, important challenges are still ahead. The most pressing is that of establishing a properly founded theory of bargaining under incomplete information. A resolution of this difficulty must presumably await a major breakthrough in the general theory of games of incomplete information. From the perspective of economic theory in general, the main challenge remains the modeling of trading institutions (with the nature of money as the most obvious target).

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.

Signaling, Forward Induction, and Stability in Finitely Repeated Games*

Abstract In a finitely repeated two-person game, suppose that after a deviation by player i from the path P in period t there is only one continuation path Q in which player i s payoff from period t on is higher than it is in P . Suppose also that player j cannot benefit from deviating from Q , whatever outcomes ensue. Then it is shown that the path P is not stable in the sense of Kohlberg and Mertens ( Econometrica 54 (1986), 1003–1037). It follows that, in a repeated game of coordination, among the set of pure outcome paths which consist of sequences of one-shot Nash equilibria, only those with payoffs very nearly Pareto efficient are stable.

ENTRY-DETERRING POLICY DIFFERENTIATION BY ELECTORAL CANDIDATES

Abstract This paper studies the equilibria of a one-dimensional spatial model in which three candidates seek to maximize their probabilities of winning, are uncertain about the voters’ preferences, and may move whenever they wish. In the presence of enough uncertainty there is an equilibrium in which two candidates enter simultaneously at distinct positions in the first period and either the third candidate does not enter or enters between the first two in the second period.

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.

Sampling equilibrium, with an application to strategic voting

We suggest an equilibrium concept for a strategic model with a large number of players in which each player observes the actions of only a small number of the other players. The concept fits well situations in which each player treats his sample as a prediction of the distribution of actions in the entire population, and responds optimally to this prediction. We apply the concept to a strategic voting model and investigate the conditions under which a centrist candidate can win the popular vote although his strength in the population is smaller than the strengths of the right and left candidates.