Hotelling was Right

This paper proves existence of a subgame perfect equilibrium in Hotelling's original (unidimensional city, linear transportation costs, uniform distribution of the consumers, two firms with identical and constant marginal cost, perfectly inelastic demand) location–price game such that in the location subgame the location choices of the firms are pure and identical. The result can be extended to variations of the original setup (multidimensional city, nonlinear transportation costs, nonuniform distribution of consumers, many firms with identical and constant marginal costs, two or more firms with nonidentical but constant marginal costs).     

On the convergence to the Cournot equilibrium in a productive asset oligopoly

We derive a feedback equilibrium of a dynamic Cournot game where production requires exploitation of a renewable asset. As in the classical Cournot model, quantity-setting firms compete in the same market for a given homogeneous good. We show that, when the asset stock grows sufficiently fast, the unique globally asymptotically stable steady state of the dynamic Cournot game corresponds to the static Cournot solution. Initial differences between firms’ production rates due to asymmetric allocations of asset stocks tend to disappear over time. When instead the asset stock grows slowly, the system does not converge to any stationary point. We also show that, within the class of linear feedback equilibrium strategies, besides the couple of strategies that stabilizes the states for every possible initial conditions, there exists another couple which is more efficient, in that it leads to higher stationary equilibrium profits for both firms, closer to the collusive outcome. Finally, we show that, as the discount rate approaches zero, there exist multiple linear feedback equilibrium strategies that induce a price trajectory that converges asymptotically to a price which is above the static Cournot equilibrium price.     

Spatial duopoly with discriminatory pricing

The concept and existence of an equilibrium is established for profit maximizing competitors whose decisions involve choices of both delivered price schedules and firm locations. Each firm faces a production function; each is allowed to locate in the plane and to set discriminatory prices. Any transport cost function that is continuous in the firm location variable may be used. It is shown that the locations of the two firms are in equilibrium if each firm is minimizing social cost (i.e., the total cost to the firms of supplying the market with the good it demands is minimized) with respect to the opponent's fixed location.     

Quality and Location Choices under Price Regulation

In a model of spatial competition, we analyze the equilibrium outcomes in markets where the product price is exogenous. Using an extended version of the Hotelling model, we assume that firms choose their locations and the quality of the product they supply. We derive the optimal price set by a welfarist regulator. If the regulator can commit to a price prior to the choice of locations, the optimal (second-best) price causes overinvestment in quality and an insufficient degree of horizontal differentiation (compared with the first-best solution) if the transportation cost of consumers is sufficiently high. Under partial commitment, where the regulator is not able to commit prior to location choices, the optimal price induces first-best quality, but horizontal differentiation is inefficiently high.     

Competition in multiple characteristics: An empirical test of location equilibrium

With products differentiated in multiple dimensions, the location equilibrium for a duopolistic market exhibits maximum differentiation in one dimension and minimum differentiation in all the other dimensions. This paper analyses whether this equilibrium arises using real data for the Spanish movie theatre exhibition market where the firms (cinemas) are differentiated along two main dimensions (their geographical location and the set of movies exhibited). Data not only shows a trade-off, in that closer theatres tend to choose a higher proportion of different movies, but also that there is a tendency towards either max–min or min–max product differentiation.     

Managerial overconfidence,overinvestment, and R&D spillover

This paper examines whether a firm will select an overoptimistic manager when a cost‐reduction investment has a spillover effect. We consider a Cournot competition model where R&D investment ex ante occurs before the process of product market competition. Our analysis reveals that there exists a unique and symmetric equilibrium for firms to delegate overoptimistic managers. We show that only when the spillover effect is sufficiently high do firms benefit from delegation. Furthermore, the equilibrium confidence level and investment decision first decrease and then increase as the spillover parameter changes. As the initial production cost increases, the equilibrium performance becomes worse.     

Existence of equilibrium in a differential game of spatial competition with advertising

We investigate a differential duopoly game with horizontal product differentiation and advertising efforts aimed at increasing market demand, to show that the standard approach to spatial competition fails to produce a pure-strategy price equilibrium in a dynamic game framework. This holds independently of the shape of the transportation cost function. Then, we introduce an endogenous cost associated with the choice of location and characterise the feedback equilibrium, identifying the necessary and sufficient condition for the existence of the pure-strategy (stationary) price equilibrium. The same condition is singled out for the static game where consumer population is constant. Finally, we show that the static game cannot be viewed as a special case of the dynamic one.     

A Positive Theory of Moral Management, Social Pressure, and Corporate Social Performance

This paper provides a theory of firm behavior motivated by moral duty, self-interest, and social pressure. A morally managed and a self-interested firm compete in a market in which their corporate social performance (CSP) provides product differentiation. Some citizens have altruistic or warm glow preferences for products with associated CSP, personal giving to social causes, holding shares in firms providing CSP, and contributing to social pressure to increase CSP. Social pressure is delivered by an activist NGO funded by voluntary contributions by citizens. The model characterizes an equilibrium in the product market, the capital market, and the market for social pressure. The equilibrium establishes a price for CSP and for activist-induced social pressure. The theory provides predictions of the market values of firms, the prices of products, firm profits, target selection, contributions to the activist, and the amount of CSP supplied. For example, if citizens do not distinguish between morally motivated CSP and CSP induced by social pressure, the activist is more likely to target the softer, morally motivated firm. Higher quality activists are better funded, target self-interested firms, and obtain greater corporate social performance. Lower quality activists target morally managed firms.     

On pure-strategy Nash equilibria in price–quantity games

This paper examines the existence and characteristics of pure-strategy Nash equilibria in oligopoly models in which firms simultaneously set prices and quantities. Existence of a pure-strategy equilibrium is proved for a class of price–quantity games. If the demand function is continuous, then the equilibrium outcome is similar to that of a price-only model. With discontinuous demand and limited spillover, there are rationing equilibria in which combined production falls short of market demand. Moreover, there might again be an equilibrium reflecting the outcome of a price game. Competition in price and quantity thus yields Bertrand outcomes under a variety of market conditions.     

Reference Dependence and Market Competition

This paper examines the implications of consumer reference dependence for market competition. If consumers take some product (e.g., the first product they consider) as the reference point when evaluating others and they exhibit loss aversion, then the more “prominent” firm whose product is taken as the reference point by more consumers will randomize between a high and a low price. We also find that consumer loss aversion in the price dimension intensifies competition while that in the product dimension softens competition. With consumer reference dependence, asymmetric prominence can arise as an equilibrium outcome when firms advertise before engaging in price competition.     

Equilibria in a class of aggregative location games

Consider a multimarket oligopoly, where firms have a single license that allows them to supply exactly one market out of a given set of markets. How does the restriction to supply only one market influence the existence of equilibria in the game? To answer this question, we study a general class of aggregative location games where a strategy of a player is to choose simultaneously both a location out of a finite set and a non-negative quantity out of a compact interval. The utility of each player is assumed to depend solely on the chosen location, the chosen quantity, and the aggregated quantity of all other players on the chosen location. We show that each game in this class possesses a pure Nash equilibrium whenever the players’ utility functions satisfy the assumptions negative externality, decreasing marginal utility, continuity, and Location–Symmetry. We also provide examples exhibiting that, if one of the assumptions is violated, a pure Nash equilibrium may fail to exist.     

On nonrenewable resource oligopolies: The asymmetric case

We give a full characterization of the open-loop Nash equilibrium of a nonrenewable resource game between two types of firms differing in extraction costs. We show that (i) there almost always exists a phase where both types of firms supply simultaneously, (ii) when the high cost mines are exploited by a number of firms that goes to infinity the equilibrium approaches the cartel-versus-fringe equilibrium with the fringe firms acting as price takers, and (iii) the cheaper resource may not be exhausted first, a violation of the Herfindahl rule, that may be detrimental to social welfare.     

Quantity precommitment and price-matching

We study the effects of price-matching in a capacity-constrained duopoly setting. We show that no firm does worse at any pure equilibrium under price-matching relative to Bertrand, but as capacity increases, one or both firms do better relative to Bertrand. If the firms choose their capacities simultaneously before making pricing decisions, then the effect of price-matching varies with the cost of capacity. Specifically, when the cost is “high” price-matching either (i) has no effect on the market price, i.e., the market price associated with the pure SPEs is the Cournot one, or (ii) weakly decreases the market price relative to Cournot. Furthermore, when the cost is “low” price-matching leads to a set of (pure) SPE prices that includes the Cournot price in the interior. Therefore, price-matching does not necessarily benefit the firms when firms select their capacities before competing in price.     

Endogenous qualifications and firms'' agglomeration

This paper analyzes firms' location when workers endogenously choose to qualify for professional skills but when they remain uncertain about the potential match between their personal abilities and/or affinities and the firms' specific production tasks. By qualifying in a region where firms agglomerate, workers benefit from higher prospects of good match. At the equilibrium, we show that firms may locate in a single cluster, symmetric clusters or even asymmetric clusters. Comparative statics with respect to product market demand and labor supply parameters are provided.     

Full or partial market coverage? A note on spatial competition with elastic demand

In this paper, a spatial model is used to endogenously determine product locations and prices when consumers have an elastic demand with a finite reservation price. I show under which condition a two‐stage Bertrand–Nash equilibrium yields maximal product differentiation with full market covering. Additionally, this paper highlights the effects of a change in the reservation price and in the utility loss rate on the equilibrium values of the model. The ambiguous effect of a change in the utility loss rate on prices constitutes a rather puzzling result. Copyright © 1999 John Wiley & Sons, Ltd.     

Upstream market structure and downstream partial ownership

Existing studies on partial ownership usually overlook the effects of vertically related markets. Our paper highlights the importance of the upstream market on downstream firms' incentives to acquire partial ownership and the consequent welfare implications. In the main model, we assume that there are three firms in the downstream market, two of which may form a partial ownership arrangement. We find several results that are in contrast to those in the literature. First, the two firms will engage in partial ownership if the upstream market is an oligopoly (triopoly or duopoly). Second, partial ownership may raise total production, consumer surplus, and social welfare. This happens when the upstream market consists of a duopoly and the two firms involved in partial ownership are supplied by different suppliers. Third, the outsider, commonly known as a free rider in the literature, may become a victim of partial ownership. Our results are robust to several extensions, including a general $n$-firm framework, product differentiation, and uniform pricing by upstream firms. We also provide the conditions under which the curvature of the demand function and the convexity of the cost function motivate firms to form partial ownership.     

Urban search models under high-relocation costs. Theory and application to spatial mismatch

We develop a search-matching model in which mobility costs are so high that it is too costly for workers to relocate when a change in their employment status occurs. We show that, in equilibrium, wages increase with distance to jobs and commuting costs because firms need to compensate the transportation cost difference between the employed and unemployed workers at each location in the city. We also show that the equilibrium land rent is negatively affected by the unemployment benefit because an increase in the latter induce firms to create less jobs, which, in turn, reduces the competition in the land market. We then use this model to provide a mechanism for the observed spatial mismatch between where black workers live and where jobs are. We finally show that a transportation policy consisting in subsidizing the commuting costs of black workers can increase job creation and reduce unemployment if the level of the subsidy is set at a sufficiently high level.     

Multi-store competition: Market segmentation or interlacing?

This paper develops a model for multi-store competition between firms. Using the fact that different firms have different outlets and produce horizontally differentiated goods, we obtain a pure strategy equilibrium where firms choose a different location for each outlet and firms' locations are interlaced. The location decisions of multi-store firms are completely independent of each other. Firms choose locations that minimize transportation costs of consumers. Moreover, generically, the subgame perfect equilibrium is unique and when the firms have an equal number of outlets, prices are independent of the number of outlets.     

When should a firm set its selling price to cope with gray market trade?

This study investigates the problem of timing for firms that must cope with gray market in setting its prices by applying an observable delay game. We consider a case in which a multinational firm sells a product in two countries, and a parallel importer buys the product in one country and resells it in the other country. We show that the multinational firm never sets its price at the same time when the parallel importer sets in equilibrium, and that the multinational firm's optimal timing depends on the degree of variation in consumer preferences for product quality.     

Information or Opinion? Media Bias as Product Differentiation

Two aspects of media bias are important empirically. First, bias is persistent: it does not seem to disappear even when the media is under scrutiny. Second, bias is conflicting: different people often perceive bias in the same media outlet to be of opposite signs. We build a model in which both empirical characteristics of bias are observed in equilibrium. The key assumptions are that the information contained in the facts about a news event may not always be fully verifiable, and consumers have heterogeneous prior views ("ideologies") about the news event. Based on these ingredients of the model, we build a location model with entry to characterize firms' reports in equilibrium, and the nature of bias. When a news item comprises only fully verifiable facts, firms report these as such, so that there is no bias and the market looks like any market for information . When a news item comprises information that is mostly nonverifiable, however, then consumers may care both about opinion and editorials, and a firm's report will contain both these aspects—in which case the market resembles any differentiated product market . Thus, the appearance of bias is a result of equilibrium product differentiation when some facts are nonverifiable. We use the model to address several questions, including the impact of competition on bias, the incentives to report unpopular news, and the impact of owner ideology on bias. In general, competition does not lead to a reduction in bias unless this is accompanied by an increase in verifiability or a smaller dispersion of prior beliefs.