The manufacturers' choice of distribution policy under successive duopoly.

• Author: Moner-Colonques, Rafael

1. Introduction

   This article investigates what the equilibrium distribution systems are in a successive duopoly when manufacturers of differentiated products with asymmetric demands choose the number of retailers they wish to employ, and both retailers can be multiproduct sellers. Two strategic decisions, the terms of payment and how many retailers to contract with, have important implications for market outcomes and consequently for the existence and the intensity of both inter- and intrabrand competition.

   It is observed that some brands are exclusively sold at a particular store while other brands can be found in several stores. Also, in many industries, such as the food retailing sector in Europe and the United States, the market is concentrated both at the manufacturing and retailing stages. These facts can be examined by considering a duopoly both upstream and downstream where retailers may carry both brands. Further, a retail duopoly permits a manufacturer to switch to another retailer, if profitable. With these facts in hand, the number of possible distribution systems is larger than in previous work in this area, including among them the well-known exclusive and common distribution systems. We are then interested in studying the strategic reasons why manufacturers may introduce intrabrand competition, particularly identifying conditions under which asymmetric distribution systems arise at equilibrium, departing from a setting with asymmetric demands.

   An interesting question addressed in the received literature on distribution systems has been whether manufacturers would prefer having a single, common retailer rather than separate exclusive retailers. These two structures, common and exclusive dealership, have been compared by Lin (1990) and O'Brien and Shaffer (1993), who show that the latter is chosen in order to dampen competition between the manufacturers. In a setting with two manufacturers and only one retailer, the central question is whether a manufacturer's brand is excluded from the market. O'Brien and Shaffer (1997) and Bernheim and Whinston (1998) prove that vertical foreclosure is not an equilibrium. Under successive duopoly, a key assumption is to permit retailers to switch to a rival manufacturer under both common and exclusive dealership. In this case, Gabrielsen and Sorgard (1999) show that manufacturers distribute their products through the same retailer. We would not want to exogenously restrict the distribution policy choice by manufacturers and thus the number of (possible) distribution systems. This leads us to contemplate the possibility of switching from the viewpoint of manufacturers. Moreover, to enrich the analysis on distribution systems, we consider asymmetric product demands to understand the effect of products with different equilibrium margins on the distribution policy choice. Hence, our analysis complements and generalizes earlier work in that manufacturers with asymmetric and differentiated brands choose how many retailers to employ and that each retailer can carry one or both products. Consequently, the introduction of intrabrand competition becomes a strategic decision for manufacturers and may coexist with interbrand competition. (1)

   The model that we examine assumes that there are two differentiated manufacturers, which are asymmetric because their products are valued differently by consumers, and two potentially identical retailers who play a noncooperative multistage game. Decisions at each stage are taken simultaneously and independently. Manufacturers play noncooperatively in the first two stages of the game. In the first stage, manufacturers choose whether to employ retailer one, retailer two, both or neither of them. That is, each manufacturer chooses its distribution policy and these choices will result in a particular distribution system. In the second stage, manufacturers decide on transfer prices. In the third stage, retailers choose quantities. Thus, we develop a model where the existence of both inter- and intrabrand competition is endogenously determined.

   Our analysis shows, in concordance with earlier work in the literature, that the well-known exclusive dealing structure arises when there is minor product differentiation and brand asymmetry. To dampen competition, manufacturers each employ a different retailer to distribute their product. However, if the degree of product differentiation were large, interbrand competition would be low. As a result, both manufacturers would withdraw from exclusive dealing and distribute through both retailers as long as the brand asymmetry was low. There is more to gain by increasing output than there is to lose from competing more aggressively. The resulting equilibrium is a very competitive situation where interbrand competition coexists with intrabrand competition in both brands. Most interestingly, there can exist equilibria with asymmetric distribution systems where the manufacturer with the most profitable brand employs two retailers while the rival employs just one. These equilibria will occur when both product differentiation and brand asymmetry are sufficiently large. Under these conditions and because products are substitutes, the multiproduct retailer internalizes the competition between the two brands in favor of the most profitable brand. In this unfavorable situation, the manufacturer with the least profitable brand will not introduce intrabrand competition, it hires only one retailer and hence the asymmetric structure arises. (2)

   The remainder of the article is organized as follows. The next section presents the model. Several subsections describe the subgame perfect equilibria of the game. Some brief concluding remarks close the article.

2. The Model

   We set up a three-stage noncooperative game to study the equilibrium distribution structure that will arise from the strategic decisions of two manufacturers, [M.sub.i], i= 1,2, and two retailers, [R.sub.k], k = 1, 2.

   The two manufacturers produce their own branded good under constant returns to scale and incur a common unit cost c. The retailers are supplied by the manufacturers at a constant unit tranfer price. Let [w.sub.i] denote the transfer price set by manufacturer i. We assume that retailers are not differentiated in the sense that consumers of brand i receive the same utility no matter which retailer k is selling brand i to them.

   In the first stage of the game, each manufacturer i chooses simultaneously and independently its distribution policy: one element [s.sub.i] from the set [S.sub.i]= {0, 1, 2, 12}. If manufacturer i chooses [s.sub.i] = 0, it does not deal with any retailer. If [s.sub.i] = 1 is chosen, manufacturer i will employ [R.sub.i] to distribute his brand; likewise for [s.sub.i] = 2. Finally, if [s.sub.i] 12 is chosen, manufacturer i will employ both retailers. Any pair of distribution policies, ([s.sub.1], [s.sub.2]), defines a distribution system. Although retailers are not differentiated, the nature of competition depends on which retailers are employed by each manufacturer. Sixteen different distribution systems may result from the manufacturers' strategic choice of retailers. In the second stage, after having observed the outcome of the first stage, manufacturers choose simultaneously and independently the transfer prices to retailers. (3) Given the outcome of the previous two stages, each active retailer k selects the quantity for each branded good they are willing to market. Denote by [q.sub.ik] the quantity of brand i that retailer k sells to consumers. Let [Q.sub.i] stand for the total amount of brand i produced, which is [Q.sub.i] = [q.sub.i1] + [q.sub.i2] when both retailers distribute that brand. As well as paying the transfers, the retailers incur retailing costs at a constant per-unit level r (for the sake of the exposition and without loss of generality, these are assumed to be zero). Also, we assume that neither manufacturers nor retailers can enforce a given distribution system by including clauses in the contract. In other words, the equilibrium distribution system is the result of strategic interaction between manufacturers and induces an equilibrium in the products' market.

   The retailers face a continuum of identical consumers. The representative consumer maximizes U([Q.sub.1] [Q.sub.2], y) subject to the budget constraint 1 = y + [P.sub.1][Q.sub.1] + [p.sub.2][Q.sub.2]. Income is denoted by 1, y is the quantity of the numeraire commodity consumed, and [Q.sub.i] and [P.sub.i], i = 1, 2, are the quantity and price of the brand, respectively produced by manufacturer i. The function U is assumed to be separable, linear in the numeraire commodity, and quadratic and strictly concave in the differentiated good: U = y + [a.sub.1][Q.sub.1] +[a.sub.2][Q.sub.2] - [b(Q.sup.2.sub.1] + [Q.sup.2.sub.2]) + 2d[Q.sub.i][Q.sub.2]]/2, where [a.sub.i], i = 1, 2, b and d are positive, b > d and [a.sub.i]b - [a.sub.j]d > 0 for i [not equal to] j. This utility function gives rise to a linear demand schedule, where inverse demands are given by

   (1) [P.sub.1] = [a.sub.1] - b[Q.sub.i] - d[Q.sub.2]

   [p.sub.2] = [a.sub.2] b[Q.sub.2] - d[Q.sub.1].

   We assume, without loss of generality, that [a.sub.1] [greater than or equal to] [a.sub.2], that the highest price (when quantities are set to zero) that consumers are willing to pay for the good produced by [M.sub.1] is greater than or equal to that for the good produced by [M.sub.2]. Also, because b > d > 0, own effects on prices are greater than cross effects. Note that the difference between b and d measures the degree of interbrand competition. Brands 1 and 2 are imperfect substitutes, but when d approaches b, brands become closer substitutes, and interbrand competition increases. Because the retailers are not differentiated, intrabrand competition is intense when both retailers carry one of the brands.

   We look for the subgame perfect equilibria of this three-stage game. As usual...