We analyze a general model in which, at each echelon of the supply process, an arbitrary number of firms compete, offering one or multiple products to some or all of the firms at the next or possibly subsequent echelons or directly to the end consumer. At each echelon, the offered products are differentiated and the firms belonging to this echelon engage in price competition. The model assumes a general set of piece-wise linear consumer demand functions for all products (potentially) brought to the consumer market, where each product's demand volume may depend on the retail prices charged for all products; consumers' preferences over the various product/retailer combinations are general and asymmetric. Similarly the cost rates incurred by the firms at the most upstream echelon are general as well. We initially study a two-echelon sequential oligopoly with competing suppliers, each selling multiple products indirectly through a pool of multiple competing retailers or directly to end consumers. In some cases, a supplier may choose to sell some or all of its products simultaneously via its direct sales channel and indirectly via some or all of the retailers. We characterize the equilibrium behavior under linear price-only contracts. In the second stage, given wholesale prices and prices of direct sales channels selected in the first stage, all retailers simultaneously decide on their retail prices to maximize their total profits among all products of all suppliers they choose to do business with. In the first stage, the suppliers anticipate the retailers' responses and all suppliers simultaneously maximize their total pro ts from all channels direct or indirect channels by selecting the wholesale prices and direct sales channel prices. We show that in this two-stage competition model, a subgame perfect Nash equilibrium always exists. Multiple subgame perfect equilibria may arise but, if so, all equilibria are equivalent in the sense of generating unique demands and profits for all firms. We subsequently generalize our results to supply chain models with an arbitrary set of echelons, and show how all equilibrium performance measures can be computed with an efficient recursive scheme. The model may, also be used to evaluate the impact of various structural changes in the supply chain network.

We analyze a general model in which, at each echelon of the supply process, an arbitrary number of firms compete, offering one or multiple products to some or all of the firms at the next echelon, with firms at the most downstream echelon selling to the end consumer. At each echelon, the offered products are differentiated and the firms belonging to this echelon engage in price competition. The model assumes a general set of piece-wise linear consumer demand functions for all products (potentially) brought to the consumer market, where each product's demand volume may depend on the retail prices charged for all products; consumers' preferences over the various product/retailer combinations are general and asymmetric. Similarly the cost rates incurred by the firms at the most upstream echelon are general as well.We initially study a two-echelon sequential oligopoly with competing suppliers, each selling multiple products through a pool of multiple competing retailers. We characterize the equilibrium behavior under linear price-only contracts. In the second stage, given wholesale prices selected in the first stage, all retailers simultaneously decide on their retail prices to maximize their total profits among all products of all suppliers they choose to do business with. In the first stage, the suppliers anticipate the retailers' responses and all suppliers simultaneously maximize their total profits from all channels by selecting the wholesale prices. We show that in this two-stage competition model, a subgame perfect Nash equilibrium always exists. Multiple subgame perfect equilibria may arise but, if so, all equilibria are equivalent in the sense of generating unique demands and profits for all firms. We subsequently generalize our results to supply chain models with an arbitrary set of echelons, and show how all equilibrium performance measures can be computed with an efficient recursive scheme. Moreover, we establish how changes in the structure of the supply chain network, or changes in the model parameters, in particular, exogenous cost rates, or intercept values in the demand functions, impact on the system-wide equilibrium. These comparative statics results allow for the quantification of cost pass-through effects and the measurement and characterization of the brand value of different retailers and suppliers.

In this book a rigorous, systematic, mathematical analysis is presented for oligopoly with multi-product firms in static as well as dynamic frameworks in the light of recent developments in theories of games, oligopoly and industrial organization. The general results derived in this book on oligopoly with multi-product firms contain, as special cases, all previous results on oligopoly with single product as well as oligopoly with product differentiation and single product firms. A constructive nu- merical method is given for finding the Cournot-Nash equilibrium, which may be extremely valuable to those who are interested in numerical analysis of the effects of various industrial policies. A sequential adjustment process is also formulated for finding the equilibrium. Dynamic adjustment processes have two versions, one with a discrete time scale and the other with a continuous time scale. The stability of the equilibrium is thoroughly investigated utilizing powerful mathematical results from the stability and linear algebra literature. The methodology developed for analyzing stability proves to be useful for dynamic analysis of economic models.

Several studies on mixed oligopoly indicate that the ownership pattern of firms does not affect the equilibrium price. This idea often suggests that ownership is irrelevant. In a mixed duopoly under price competition, firm ownership is irrelevant. This study reveals that ownership is irrelevant in a single publicly owned firm and in any positive number of privately owned firms. However, if two or more publicly owned firms exist, then ownership becomes relevant in a homogeneous good market with a strictly increasing convex cost schedule and a downward sloping demand curve. If firms set the price sequentially and if the lone public firm is a price leader, then social welfare is constantly greater than when the latter is a price follower. The unique price is the competitive price when the public firm moves first in the sequential game.

This research investigates three issues related to the economic performance of oligopolistic markets where firms produce differentiated products and compete in prices. First of all, this dissertation uses a Markov Perfect Equilibrium approach with fixed periods of commitment of actions to answer the question of what prices a duopolists will charge in equilibrium if they produce horizontally differentiated products, move alternatingly, and compete in prices forever. It is found that firms charge prices which are higher than Nash equilibrium prices but lower than the fully collusive equilibrium prices. Also, contrasted with the Nash equilibrium of the one-shot constituent game, the firm having the significantly higher demand responsiveness to its own price always charges a lower price than the other firm does although it has higher marginal cost. The dissertation then proceeds to study whether a firm can overcome its cost disadvantage by upgrading its product over the rival's, and if so, whether there exists a profit-division which will induce the low cost firm and the high cost firm to collude and no one has an incentive to cheat. The results show that (1) the ability of upgrading the product over the rival's can allow a high cost firm to earn higher profit than a cost advantaged low cost firm; (2) there exists at least one profit-division which can sustain full collusion; and (3) in the collusive equilibrium firms enlarge their quality differences to alleviate the price tension between their products. Finally, this work investigates the welfare effect of mergers which occur in an oligopolistic industry where firms produce differentiated products. It is shown that for the merger to be socially beneficial, the number of the merging firms must be less than the total number of firms in the industry minus the ratio of the products' own elasticity to cross elasticity. The analysis indicates that the welfare effect of a merger of a specific size depends on the substitutability among products of the industry.

The thesis consists of five chapters. The first of them contains introduction. Chapter 2 considers a broad class of two player symmetric games, which display a fundamental non-concavity when actions of both players are about to be the same. This implies that no symmetric equilibrium is possible. We distinguish different properties of the payoff functions, like strategic substitutes, complements and quasi-concavity, which are not necessarily imposed globally on the joint action space. A number of applications from industrial organization and applied microeconomics literature are provided. In Chapter 3 we generalize to the extent possible the known results for the case of games with one-dimensional action sets to the general case of games with action spaces that are complete lattices. We find that in the general case the scope for asymmetric equilibrium behavior is definitely broader than in the one-dimensional case, though still quite limited. Moreover, we investigate under which sufficient conditions asymmetric pure strategy Nash equilibria are always Pareto dominated by symmetric pure strategy Nash equilibria. In Chapter 4 we deal with the effects of market transparency on prices in the Bertrand duopoly model. We consider two types of strategic interaction between firms in an industry - strategic complementarities and substitutabilities. In the first case, the results are close to conventional wisdom, especially, when in the same time products are substitutes. Namely, equilibrium prices and profits are always decreasing in transparency level, while the consumer’s surplus is increasing. Considering price competition with strategic substitutes, an ambiguity in the direction of change of prices appears. This leads to ambiguity concerning equilibrium profits and surplus changes caused by increasing transparency. In Chapter 5 we provide general conditions for Cournot oligopoly with product differentiation to have monotonic reaction correspondences. We give a proof for the conditions stated by Vives (1999). Moreover we elaborate more general requirements. They allow for identifying increasing best responses even in case inverse demand is submodular, and similarly, decreasing best responses in case of supermodular inverse demand. Examples illustrating the scope of applicability of these results are provided.

The theory of price and quality decision-making in industries with a few firms which recognize their mutual interdependence is of increasing interest to economists and policy makers. This book introduces a novel theory of that decision-making, based upon the notion of the industry as a community of agents who are involved in both competitive and cooperative relationships. It develops theories and illustrates methodological approaches to the analysis of price and quality decision-making in such instances of a 'rivalrous consonance of interests' among firms.