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Author: Awi Federgruen Publisher: ISBN: Category : Languages : en Pages : 54
Book Description
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.
Author: Awi Federgruen Publisher: ISBN: Category : Languages : en Pages : 54
Book Description
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.
Author: Awi Federgruen Publisher: ISBN: Category : Languages : en Pages : 50
Book Description
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.
Author: Amarjyoti Mahanta Publisher: ISBN: Category : Languages : en Pages : 16
Book Description
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.
Author: Shyh-Fang Ueng Publisher: ISBN: Category : Competition Languages : en Pages : 118
Book Description
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.
Author: Robert E. Kuenne Publisher: Springer ISBN: 0230503713 Category : Business & Economics Languages : en Pages : 442
Book Description
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.
Author: Guillermo Gallego Publisher: ISBN: Category : Languages : en Pages : 26
Book Description
We study firms that sell multiple substitutable products and customers whose purchase behavior follows a Nested Logit model, of which the Multinomial Logit model is a special case. Customers make purchasing decision sequentially under the Nested Logit model: they first select a nest of products and subsequently purchase one within the selected nest. We consider the multi-product pricing problem under the general Nested Logit model with product-differentiated price sensitivities and arbitrary nest coefficients. We show that the adjusted markup, defined as price minus cost minus the reciprocal of price sensitivity, is constant for all products within a nest at optimality. This reduces the problem's dimension to a single variable per nest. We also show that the adjusted nest-level markup is nest-invariant for all the nests, which further reduces the problem to maximizing a single-variable unimodal function under mild conditions. We also use this result to simplify the oligopolistic multi-product price competition and characterize the Nash equilibrium. We also consider more general attraction functions that include the linear utility and the multiplicative competitive interaction models as special cases, and show that similar techniques can be used to significantly simplify the corresponding pricing problems.
Author: Koji Okuguchi Publisher: Springer Science & Business Media ISBN: 3662026228 Category : Business & Economics Languages : en Pages : 177
Book Description
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.
Author: Awi Federgruen Publisher: ISBN: Category : Languages : en Pages : 49
Book Description
We address a generic price competition model in an industry with an arbitrary number of competitors, each offering all or a subset of a given line of N products. The products are substitutes in the sense that the demand volume of each product weakly increases whenever the price of another product increases. The cost structure is linear, with arbitrary cost rates.Our demand model is the unique regular extension of a set of demand functions that are affine in a limited polyhedral subset of the price space. A set of demand functions is regular if it satisfies the following conditions: under any given price vector, when some product is priced out of the market, i.e., has zero demand, any increase of its price has no impact on the demand volumes. Depending on the set of prices selected by the competing firms, a different product assortment is offered on the market.We characterize the equilibrium prices, product assortment and sales volumes in the price competition model, under this demand model. Under minimal conditions, we show that a pure Nash equilibrium always exists; while multiple price equilibria may arise, they are equivalent in the sense of generating an identical product assortment and sales volumes.
Author: Awi Federgruen
Author: Awi Federgruen
Author: Awi Federgruen
Author: Amarjyoti Mahanta
Author: Shyh-Fang Ueng
Author: Robert E. Kuenne
Author: Guillermo Gallego
Author: Koji Okuguchi
Author: Kōji Okuguchi
Author: Junichi Watanabe
Author: Awi Federgruen