I. Introduction

Economic models of collusion are central to antitrust policy. Besides their direct application to price-fixing and "conscious parallelism" cases, the analyses of the Department of Justice Merger Guidelines and the Department of Justice Vertical Restraint Guidelines rely heavily on the collusive model.' One of the reasons for its central role is an intuitive appeal. Collusion has the potential to maximize the overall profits of firms in an industry. In addition, the collusion model yields a number of direct implications for evaluating the likelihood of anticompetitive behavior. One of the standard implications is that collusion is less likely in industries characterized by product differentiation.? In such industries, it is claimed that a more complex set of prices must be established and enforced for collusion to be effective. This claim may have a substantial impact since many of the markets subject to antitrust investigation are composed of differentiated products.' Nevertheless, it depends on the special assumption that each firm's product competes on equal terms with all other brands in the industry, i.e., competition between each brand is symmetric. Indeed, the symmetry assumption underlies other well-known implications of the collision model, including the basic tenet that collusion is more likely in concentrated industries. The effects of product differentiation may differ when firms compete more directly with some rivals than others. This possibility is embedded in spatial models of competition, where competition is highly asymmetric or localized to particular firms in the industry. While traditionally defined in terms of geographic location, spatial models of competition also represent those markets where competition depends upon the combination of product characteristics contained in different brands or qualities of the good." In these models, differences among firms' products can be functionally specified by consumers and consumers are diversified in their preferences for specific brands. The emphasis on "niche" and "segmented" markets in the marketing and corporate strategy literature suggests that many markets have these properties." It is also our experience from antitrust investigations that firms often identify specific rivals in their "market" as their closest competitors. In this article, we consider the implications of localized competition. Our analysis suggests that product differentiation may not be a hindrance to collusion when competition is localized. Indeed, a number of factors may encourage collusion. We find that asymmetric competition often makes cheating easier to detect and punish, and the gains to cheating small relative to the benefits of collusion. In addition, a collusive arrangement may be successful even if it involves only a subset of firms in the industry. Consequently, collusion may be successful even in unconcentrated markets if competition is asymmetric. We discuss standard models of collusion in section II and models of asymmetric competition in section III. We then turn to asymmetric competition and collusion. We examine the effects with fixed location and no entry in section IV and with entry and relocation in section V. Concluding comments and a discussion of limitations are in section VI.

II. Collusion with symmetric competition

Collusive schemes may range from a cartel, in which collusion is explicit, to conscious parallelism, in which collusion is implicit or tacit. A common feature of these outcomes is that firms jointly withhold output to raise prices and increase profits. Successful implementation, however, is subject to common problems; collusion violates antitrust laws, and firms can increase their individual profits by holding out from the collusive scheme or "cheating" on the collusive price to expand market share. In deriving policy implications, economists have focused on the incentives to deviate from a collusive scheme. A seminal paper by Stigler examines the ability to detect price-cutting when collusion is explicit.! More recent contributions examine conditions under which firms acting independently would arrive at tacit collusion through repeated contact." These strands of literature typically assume that competition is symmetric; product markets are either homogeneous or "Chamberlinian." In Chamberlinian models, a "representative consumer" purchases each differentiated product in the market. Consequently, each consumer simultaneously considers the price of all products, and each firm's profits depend equally upon the price of every other firm's products.w As in a homogeneous good market, a given firm competes on equal footing with all firms in the industry. A Chamberlinian notion of product differentiation underlies the hypothesis that collusion is less likely in industries with heterogeneous products. In such industries, collusion becomes more difficult due to coordination problems. For example, the 1984 Merger Guidelines state, As the products which constitute the relevant product market become more numerous, heterogeneous, or differentiated, the problems facing a cartel become more complex. Instead of a single price, it may be necessary to establish and enforce a complex schedule of prices. (section 3.411) Implicit in this statement is the notion that firms must agree on a complete schedule of prices and product quality for each firm's products. In addition, cheating may be harder to detect, since a cheating firm can modify product attributes as well the price. Symmetry plays a central role in the fundamental belief that collusion is more likely in concentrated industries. In an industry with symmetric competition, all or at least most firms in the industry must be included in a collusive scheme for it to be effective.? Therefore, as the number of firms increases, the profits from collusion must be split more ways, so that the gains to collusion are smaller. The costs of coordinating a collusive scheme are also likely to increase with the number of participating firms since the agreement is more difficult to reach. The number of firms may also affect the ability to detect cheaters. When a single firm is cheating in an industry with N colluding firms, the probability that any one firm is cheating is liN when competition is symmetric. Therefore, the likelihood of detecting a cheater decreases with the number of firms."

It might seem that the numbers problem or the differentiated product problem could be overcome by limiting the size of the cartel. However, when competition between firms is symmetric, a cheating or hold-out firm disrupts the entire collusive scheme. In an industry with N firms, a reduction in price by one firm draws customers from all of the other N-l firms in the industry, so that each non colluding firm has the potential to greatly increase profits at the expense of other firms. Therefore, the majority of industry output must be under the control of colluding firms if a collusive scheme is to be effective. Another important condition for collusion to be effective is that entry must be sufficiently difficult so that profits are not quickly eroded when the price is raised. The assumption of symmetric competition then implies that an entrant causes each firm in the industry to lose profits. Similarly, any action that deters entry benefits all established firms, so joint action may be required to overcome the costs of erecting entry barriers. In sum, the ability to maintain collusion decreases with the number of firms in the industry when competition is symmetric. Each firm in the industry must participate if the collusive scheme is to function well. Otherwise, the hold-out or price-cutting firm may cheat any of the other firms with equal facility. Product heterogeneity is likely to compound these problems, due to greater difficulty in establishing price schedules and monitoring product variations.

III. Models of asymmetric competition.

The essential characteristic of markets with asymmetric competition is that the location of each firm's product matters to consumers. Location is commonly viewed in terms of physical distance but may be taken more broadly to mean distance along a spectrum of product characteristics or quality. For example, computers are ranked in terms of objective characteristics such as computation speed, memory, and other attributes. Sometimes, a bundle of consumer characteristics may be usefully reduced to one dimension, such as quality. For example, a 1966 Lafite-Rothschild may be at one end of the wine spectrum, and Thunderbird (any year) may be at the other. For simplicity, we at first limit the analysis to the competition along one dimension. In spatial type markets, consumers have preferences for products at particular locations in geographic or product space and are willing to pay more for products at their more desired locations.v For example, it is less costly for a consumer to purchase from a nearby location than a more distant one. This is particularly true for frequently purchased small-ticket items, such as food products or gasoline. When location refers to product characteristics or quality, consumers have preferences for particular items because of their income, prestige value, characteristics of complementary goods that they own (e.g., software compatible with a computer, or a part for an appliance), or just idiosyncratic tastes. In markets where location matters, competition tends to be "localized" in the sense that a firm only competes directly for customers of neighboring firms. To see this, assume that consumers are located uniformly along a line, while firms sell the same product but are located at different points. Assume there are five firms, such as A, B, C, D, and E portrayed in figure 1. If a firm sets price p for its product and all consumers incur a cost t per unit distance of transporting the good, the total cost or delivered price to a consumer purchasing the good x units from the firm is p+tx. I S. The antitrust bulletin Figure 1

if all firms set the same price, customers at different points purchase from the closest firm. As can be seen in figure 1, line IJ and IK represent the delivered price to consumers at various distances from firm C. Consider point z. Consumers between z and C purchase from firm C, and consumers between z and B purchase from firm B. By lowering its price, firm C attracts some customers (those immediately to the left of z) that formerly purchased from firm B. A reduction in firm C's price would shift the delivered price schedule to I'J' and I'K', and firm C would attract customers between z and z'. Analogously, firm C would also attract some customers of firm D. Thus, a change in one firm's price directly affects only neighboring firms.ts The same principles apply to competition in goods that are distinguished by brand characteristics. A consumer's location then identifies its brand preferences, and the cost t represents the "disutility" to consumers from purchasing a brand type that is different from their most desired point. 11 In the above example, direct competition is localized to neighboring firms producing closer substitutes. More distant firms may, nevertheless, affect competition. In the example above, firm C's direct competitors are Band D. Other firms, such as A or E, have indirect effects, since their price affects the price set by firms B and D. Thus, if firm A lowers its price, firm B loses customers. Hence, firm B may respond by lowering its price, which, in turn, reduces the demand for C's product. Similarly, firm A may react to a price change by firm C as relayed through firm B. If firms A, B, C, D, and E are close enough competitors to each of their neighbors, they may all be affected directly or indirectly when one of them changes its price. Consequently, they may be included in the same economic market based on the notion of a close "chain of substitutes" between pairs of firms. While this approach is often adopted in antitrust analyses, firms are clearly more directly affected by some firms than others. This is the basis of the idea that competition is localized. A number of ingredients are necessary for competition to be localized. First, products must be sufficiently different from each other in the eyes of consumers. The dispersion of consumer locations or preferences must be great enough so that only a limited subset of customers respond to small price changes. Second, the number of characteristics that matter to consumers must also be sufficiently small so that the dimensions of competition are limited. If firms compete over several different product dimensions, the number of firms competing for customers at a particular location may increase. However, the dimensionality of a spatial model is determined by the number of attributes that consumers use to evaluate a product, and not necessarily the number of attributes that distinguish brands. For instance, spatial competition may exist on a relatively small number of dimensions when consumers combine a number of product attributes into an index or rank attributes in a specified order (such as a quality index). When the price is reduced in a quality setting, customers are attracted from firms that are next highest and next lowest in quality. For example, a reduction in the price of a luxury car, such as a Lexus, is likely to attract potential BMW and Infiniti buyers, but not those in the market for a Yugo. 18 Similarly, the sellers of parts or accessories for a particular brand of computers, electronics goods or appliances may only sell and compete with other suppliers specializing in that brand. In general, competition is considered localized when a firm competes more directly with certain rivals. There must, however, be some customer overlap, or else each firm has a monopoly. A final ingredient for the localized competition is that firms must be sufficiently committed to particular locations so that they are unable to acquire new customers by simply relocating. Otherwise, any firm becomes a potential competitor and competition is no longer localized.

IV. Localized competition and collusion with fixed locations.

In this section, we assume that the number and the location of firms are fixed. We show that in a market with asymmetric competition, collusion may be limited to a subset of firms and cheating firms may be easier to identify and punish. We also show that localized competition serves to reduce the returns to cheating by dampening the effect of a price cut. We begin with firms selling at a single location, and then consider firms selling at multiple locations.

A.

Single location firms We saw above that a large proportion of firms in markets with symmetric competition must participate in a collusive scheme for it to be successful. By contrast, when competition is asymmetric, the number of required participants may be small. Indeed, as few as two neighboring firms may be able to profitably collude even when other firms form a chain of "close substitutes." For example, if firms C and D in figure 1 collude, then each firm has effectively eliminated half of its direct competition. Instead of being surrounded by competitors, each firm now faces competition on only one side. As the two firms simultaneously raise prices, they lose half as many customers as to when acting independently.w The loss of customers is further reduced as nearby non colluding firms raise their prices in response to the higher prices. The pattern of delivered prices when firms C and D collude is portrayed in figure 2. The common industry price before collusion is PO. Firms C and D raise their price to PC+D after collusion, and firms Band E and firms A and F raise their prices by progressively smaller amounts as the distance from the merger increases.

Figure 2 Prices When Firms C and D Collude

Adding a third colluding firm may be feasible and even more profitable. Because market power is derived from the control of a contiguous market area, a small coalition among neighboring firms can potentially wield significant market power over localized markets. As the number of neighboring firms that collude increases, the price increase becomes larger for the most internal firm (i.e., those most isolated from non colluding firms). For example, if the collusive scheme extended to firms B, C, and D, then firm C would be completely isolated from direct competition. The colluding firms could raise prices substantially at location C without losing customers. Average profits per firm also increase. 22 Thus, even if firms A, B, C, D, and E are close competitors with each of their neighbors, a subset of these firms may profitably collude. Similar results hold in markets distinguished by differences in product characteristics or quality, as long as collusion involves those firms that compete more directly for the same customers. When a limited number of participants can profitably collude, reaching an agreement and policing cheaters may be less difficult. "Hold-out" or cheating firms may simply be omitted from the collusive arrangement. Policing cheaters on a collusive scheme are facilitated in spatial markets since a reduction in price will initially lure customers only from neighboring farms on the geographic or product spectrum. The price must be lowered enough for the customers at more distant locations to incur the higher costs of transportation or the disutility associated with patronizing more distant firms. Therefore, when transportation or disutility costs are significant, large price cuts are necessary to substantially increase market share. Since large price reductions "eat into" profits, cheating is discouraged. Even if firms are prone to cheat, such behavior may be easily detected in markets with the localized competition. Compared to a market with symmetric competition, each firm can more easily identify the source of cheating and inflict punishment. A large loss of customers is likely to result from a price reduction by a firm's closest competitors. In comparison, any of the firms in an industry with symmetric competition may be the culprit with equal probability. In addition, since firms producing more closely related products gain the most from colluding, they may be more willing to share information. In our spatial example, if firms A and C in figure 1 share information, they surround firm B and can monitor price-cutting activities from two vantage points. Consequently, prices may be more easily monitored than in markets with the symmetric competition. Localized competition may also facilitate the punishment of price cutters. If a firm cheats in a spatial setting, firms producing the closer substitutes must inflict punishment. These are precisely the firms that experience the greatest gains from deterring the nearby cheater. If these firms can price discriminate, punishment can be directed only to the offending price cutter.> Further, firms may be more willing to mete out tougher punishment if they have better information about the source of cheating. Thereby, cheating would be easier to deter.

B. Multilocation firms

Firms in a spatial setting often control plants or stores at multiple locations. For example, retailers often franchise or own chain stores serving customers in dispersed locations.> When products differ in terms of characteristics or quality, firms may offer a range of products to "satisfy their customers' needs." Such firms may have further incentives to collude. A firm controlling neighboring locations effectively forms a two-firm cartel without the headaches of coordinating separate firms. Advantages may also accrue to two non-neighboring but nearby locations (e.g., firms Band D in figure 1). A firm internal to those locations (e.g., firm C) faces no direct competitors on either side once it decides to collude with the surrounding multilocation firm. Thus, a firm internal to a cartel will be able to significantly raise the price, and, therefore, could be more easily induced to join a cartel. Control over multiple locations or product varieties may also reduce the gains from cheating. Above, we saw that except for large price cuts, the gain in customers is only from neighboring firms. If neighboring firms are jointly controlled, the gains from cheating accrue from only a single side of each location." The gains from small price cuts still accrue to a firm with locations A and C, but gains from undercutting firm B are considerably reduced. Thus, the gains from cheating are also reduced for large price cuts. A firm with multiple locations may also be in a position to more effectively monitor other firms. When locations Band Dare jointly controlled, they surround firm C. Since price cutting is monitored from two vantage points, the multilocation firm can completely isolate firm C as the source of cheating. Thereby, cheating is more quickly discovered. Similarly, firms may better coordinate punishment. Surrounding locations must inflict punishment against price cutters in spatial markets. If firms Band D independently receives different information on prices or profits, one of these firms may fail to punish cheating by firm C. Under joint control, they would punish together. Gains from improved monitoring and punishing capabilities may be especially great when the multilocation or multiproduct firm surrounds a "maverick" firm that threatens to hold out or to cheat. By itself, the firm could isolate and punish the maverick firm. Even in the absence of a single perpetrator, a firm with dispersed locations has an overview of the market. That firm has multiple vantage points from which to monitor cheating firms and to quickly retaliate. The firm may act as a cartel ringleader.

V. Localized competition and collusion with relocation and entry.

Entry and relocation may restrict the ability of firms to effectively collude. When entering into the market is easy, prices are eventually driven downward to more competitive levels. In addition, markets with the localized competition may be susceptible to repositioning by existing firms toward areas of the market with higher prices. This reaction also serves to reduce prices. When only a subset of firms in the market colludes, nonparticipating firms may attempt to reposition themselves between the colluding firms or just outside the colluding firms. If a firm repositions itself between colluding firms, the cartel dissolves at those locations and prices fall. Unless one of the incumbent firms relocates, prices may even fall below their collusive level.v A more likely scenario is for a firm to reposition itself just outside the colluding parties, where prices are highest." Nonetheless, firms near that location still lose market share and prices would fall. Just as with relocation, entry is likely to occur near the boundary of the colluding parties. Again, entry between the colluding firms will disrupt collusive pricing, thereby reducing the profitability of that strategy. Unless all firms in the industry engage in collusion, entry is more likely to occur near the boundary of colluding firms. Entry and relocation may be deterred or delayed in markets with asymmetric competition when firms face significant location-specific investments.w Some examples are heavy equipment (e.g., fixtures, refrigeration systems, inventory, etc.), machinery or technological knowledge specialized to particular product lines, long-term leases, patents, zoning approvals, licenses, knowledge of specific customers, or advertising costs of informing customers likely to purchase from particular firms. The presence of location-specific assets may have several entry-deterring effects. First, location-specific assets serve as a credible commitment that the incumbent firm will remain in the market at a particular location. Consequently, the entrant or relocating firm would continue to face competition at its new location. Second, location-specific investments generally involve fixed costs. As a result, a potential entrant must sell enough at the post-entry prices to cover these costs but is limited by competition from closely related products. Third, entry or relocation becomes riskier with significant location-specific investments. If a firm enters or relocates and subsequently found its location unprofitable, it would fail to recoup the value of those assets. Since the presence of significant location-specific assets makes entry more difficult, firms may increase such investments for the purpose of entry deterrence. This tendency for strategic investments is enhanced in markets with the localized competition since the gains are also better internalized by the firm. Certain types of behavior may also be used to frustrate entry or relocation. In a market with symmetric competition, a predatory firm must increase output by enough to lower prices throughout the market. When competition is localized, predatory prices can be directed at particular firms; the predatory firm needs only flood a segment of the market. Any costs of predatory pricing are further reduced if firms can price discriminate in order to target particular entrants. In addition, vertical integration or some type of vertical relationship (e.g., exclusive buying arrangements or exclusive territories) may be targeted to essential distribution outlets or input sources of nearby rivals." Advertising messages may also be targeted to customer locations desirable to rivals. A firm with multiple locations may have additional incentives to deter entry. Each predatory act at a particular location may set a deterrent precedent in other Locations. Alternatively, a firm with multiple locations may blanket the region, and space locations close enough together to preempt firms from being able to profitably enter. These market preemption strategies tend to be most effective when significant location-specific investments make entry and exit more difficult. In summary, while entry and relocation may dampen the effects of collusion, firms may take advantage of the conditions inherent in markets with asymmetric competition to discourage or forestall entry and relocation. A firm at a particular location may attempt to "protect its turf" by making location-specific investments or engaging in other entry-deterring conduct.

VI.

Conclusion and policy implications.

We have challenged the notion that product differentiation reduces the likelihood of collusion. Compared to homogeneous product markets, cheaters are often easier to detect and punish, the gains to cheating are often small relative to the benefits of collusion, and firms may be better able to erect entry barriers. In addition, it may be easier to organize a collusive scheme, since only a subset of firms in the market needs to participate. These conclusions arise when competition is sufficiently localized in a sector of the market. Therein lies the difference between earlier analyses suggesting that product differentiation would inhibit collusion. Firms must compete more directly with certain rivals, and the number of such rivals must be limited. In a world of uncertainty, firms must have sufficient knowledge of their own customer base and that of competitors. The ability to collude increases when the lines of competition are few in number and clearly drawn. However, firms must not be "too" different, or they may be less likely to reach an agreement on a collusive scheme or may already have sufficient market power so that collusion yields little additional benefit (especially in light of potential antitrust repercussions). Thus, firms must have some potential customer overlap, but that overlap must be limited mostly to specific firms in the industry. These results suggest a number of interesting implications for markets with the localized competition. Our analysis illustrates how the concept of "submarkets" can be given economic substance in assessing the likelihood of collusion among a subset of firms in the industry. Each firm in figure 1 may be considered part of the "economic market" as long as the firm is a close enough competitor with its neighbors. Yet, the relevant antitrust market may 368 The antitrust bulletin include a subset of firms, because anti-competitive price increases may originate from and be largely confined to a segment of the market. Two independent gas stations on adjacent corners may not face competitors for several miles, even if there are more distant stations in the same town. Similarly, while there may be many software firms, collusion may be effective among a subset of firms producing software specialized to a particular application (e.g., medicine or economics). Some of the usual indices of anticompetitive behavior may require modification in markets with the asymmetric competition. Industry concentration, usually measured for a market composed of a close chain of substitutes, may be of limited relevance when competition is localized. In spatial markets, the ability to create collusive arrangements in segments of the market becomes paramount. The degree of competition between particular firms must be considered. Entry must also be evaluated from a modified perspective. The location of the prospective entrant becomes critical. Entry at distant locations may have only a small impact upon price, while entry near the colluding parties is more likely to dampen anticompetitive effects. Further, firms must have committed assets whose value is specific to their geographic location or their location on the characteristic or quality spectrum.

Please answer the following Questions

1. The introduction paragraph, which summarizes the research's objective and specific question/s investigated in the study);

2. A summary of the study's major findings;