اثرات جانبی شبکه ها، تبعیض قیمت و دزدی سود آور

Recent papers have argued that a monopoly firm might be able to maximize its profit by allowing some customers to steal its product. In particular, with network externalities, it is claimed that allowing piracy can be profitable because it increases the user base of the product and raises the willingness-to-pay of other customers. In this paper we analyze these claims when the producer can freely choose the degree of piracy prevention. We consider profit maximizing equilibria and show that allowing piracy cannot raise profits if the monopoly producer can directly price discriminate between potential-pirates and other customers. In the absence of price discrimination, allowing piracy will only maximize profits when the ability to pirate is inversely related to customer willingness-to-pay. Even in this situation, there is no profit maximizing equilibrium where some potential pirates buy while others pirate the product. Thus, even though potential pirates differ in their ability to illegally gain the product, the profit maximizing outcome involves either no piracy or complete piracy.

The idea that a firm can maximize its profits by allowing some consumers to steal its product seems perverse. But when considering patents, copyright and the protection of intellectual property (IP), the case for ‘profitable piracy’ has been forcefully made in a number of recent papers beginning with Conner and Rumelt (1991). Of course, if complete prevention of piracy is very costly, it will usually be optimal for firms to allow some piracy. Whenever there are high enforcement costs, there will be an optimal level of any illegal activity.1 Similarly, if copying technology is cheaper than the marginal cost of ‘original’ production, then selling one unit at a high price to a group of consumers who then copy can be more profitable than selling an ‘original’ to each individual customer (Besen and Kirby, 1989). However the recent ‘profitable piracy’ claims take a different approach, arguing that allowing some piracy can be profit maximizing in the presence of network externalities.2 Three lines of argument relating ‘profitable piracy’ and network externalities have been presented in the literature. First, piracy can maximize profits for a single firm because it increases the user base of the product. With network externalities, this means that non-pirates are willing to pay more. By allowing some piracy, the seller can raise the price to paying customers and more than make up for any lost sales (see Conner and Rumelt, 1991; Takayama, 1994; Slive and Bernhardt, 1998). Alternatively, piracy can be a commitment device for a firm. Allowing piracy today can alter the firm’s incentives in the future and can limit the standard problems that face a durable goods monopoly (Takayama, 1997). Finally, piracy can be used strategically as a device to undermine the appeal and market share of competitors (Shy and Thisse, 1999). In this paper we examine the first of these claims. When there are network externalities between customers, can it be profit maximizing for a single firm to allow piracy because it increases the willingness to pay of non-pirates? And if allowing piracy can be a profit maximizing strategy, what are the minimal requirements for this to occur? In other words, is ‘profitable piracy’ a myth and, if not, when will it be observed? Understanding the case for ‘profitable piracy’ is important because it flies in the face of much observed business behavior. The piracy of intellectual property and illegal copying of copyright material is a major issue in international commerce and relations.3 Companies are developing and adopting sophisticated anti-piracy technologies to protect their copyright material. For example, music and video companies have introduced new protection devices to prevent copying of their product by computer.4 Sony has recently begun selling digital televisions with a Digital Video Interface that limits home recording.5 Piracy concerns have led to tighter laws and high profile court cases. The most prominent of these is the legal action against the music-sharing company, Napster. The Digital Millenium Copyright Act in the US has been used to prosecute a Russian programmer and Elcomsoft, his employer, for writing software that circumvents security procedures in Adobe e-books.6 At the same time, the use of ‘give-aways’ and low pricing for early adopters has been used by firms, for example, in the mobile telephone industry. To understand the relationship between ‘profitable piracy’ and network externalities for a single firm, consider a simple application from the standard literature on price discrimination.7 Suppose there are two consumer groups—customers with a high willingness-to-pay for the relevant product (high-type customers) and customers with a low willingness-to-pay (low-type customers). If a seller is unable to price discriminate between the two groups and there are relatively few customers with a low willingness-to-pay then (even in the absence of piracy) profit maximization can involve the seller setting a price above the maximum willingness-to-pay of the low-type customers. Lowering the price to sell to some of the low-type customers means lowering the price to all customers and while sales will rise, profit can fall. Now, suppose that (a) there is a network externality so that high-type customers are willing to pay more if low-type customers also have the product and (b) the low-type customers can pirate the product but the high-type customers cannot pirate. It then pays the seller to allow all low-type customers to pirate the product even if piracy could be freely prevented. After all, the customers who pirate the product were not going to buy it anyway, while increasing the customer base raises the willingness-to-pay of non-pirates. The seller, by allowing piracy, can increase prices and maximize profits. Piracy is profitable. This simple interaction between price discrimination and piracy lies at the heart of the papers by Conner and Rumelt (1991), Takayama (1994) and Slive and Bernhardt (1998).8 It is based on four specific assumptions: • customers have a differential ability to pirate; • the seller does not have an ability to directly price discriminate between different customers; • the number of potential pirates is relatively small; and • the ability to pirate is inversely correlated with customer willingness-to-pay. In this paper we develop a simple model to show that these four assumptions are not simply convenient but are necessary for a firm to find it profit maximizing to allow piracy. If any one of these four assumptions breaks down then the argument linking user base, the price to non-pirates and profitable piracy also breaks down. In this sense, the profitable piracy claims made by Conner and Rumelt (1991) and others are simply an extension of standard price discrimination.9 Our model involves two types of customers, each characterized by a distribution of consumer values and ability to pirate. The seller can freely prevent piracy.10 There is a network externality in that consumers’ values are rising in the number of people who have the product. In this framework we show: (1) if customers are ex ante identical then the seller will not allow any piracy in a profit-maximizing equilibrium; (2) if some customers have a greater ability to pirate but the seller can price discriminate between customers then the seller will not allow any piracy in a profit-maximizing equilibrium; (3) if some customers have a greater ability to pirate but the ability to pirate is independent of willingness-to-pay, then the seller will not allow any piracy in a profit-maximizing equilibrium; (4) if some customers have a greater ability to pirate, the seller cannot price discriminate, the ability to pirate is inversely related to the willingness-to-pay, and there are sufficiently few potential pirates, then the seller may allow piracy in a profit-maximizing equilibrium. However, in this case, the seller will allow piracy by all potential pirates, even though they may differ ex post in their ability to pirate and their willingness-to-pay. There is no profit maximizing equilibrium where some potential pirates buy the product while others pirate the product. The main contribution of this paper is to clarify the relationship between ‘profitable piracy’ and network externalities that have emerged in the literature. In particular, by establishing the minimal conditions for profit-maximizing piracy in a simple model, we allow both a better theoretical understanding of profitable piracy and provide pointers for empirical analysis of industry. In doing this, we resolve the apparent conflict between ‘profitable piracy’ and the strong reactions of many firms against copyright violation and IP piracy in industries where we would expect network externalities to be present. Piracy is a substitute for price discrimination and it will only be profitable for firms to exploit the feedback from piracy to user-base when price discrimination is impossible and potential pirates have specific characteristics. Our work joins a number of others who have questioned the recent ‘profitable piracy’ claims. Hui and Png (2001) estimate the relationship between the demand for music CDs and piracy. While they find that the effect of piracy on music sales is lower than industry claims, their results also suggest that piracy has, overall, an adverse impact on music companies. Tze and Poddar (2001) develop a model where firms can either completely eliminate piracy or allow a rival firm to sell an imperfect copy. In their framework, allowing piracy is never desirable. Their model is not, however, designed to capture the simple price discrimination logic that underlies the claims of profitable piracy. In this sense, their results go too far to dismiss profitable piracy. Rather, we show that allowing piracy can be profitable, but only in specific circumstances when it simply reflects well-known results regarding price discrimination. The remainder of this paper is organized as follows: the next section develops the model of piracy. Two further sections then analyze the potential for profitable piracy when price discrimination is and is not possible. A final section concludes.

In this paper we have developed a simple model to analyze the proposition that, in the presence of network externalities, a firm’s profits can increase if that firm allows some consumers to pirate its products because this raises the user base and the willingness-of-pay of other customers. We have shown that this concept of ‘profitable piracy’ depends critically on certain assumptions about both the customers’ and the firm’s behavior. In particular, in a profit maximizing equilibrium, piracy, from the perspective of a single firm, is always dominated by price discrimination. If the firm can differentiate customer prices on the basis of ability to pirate, then this is always preferred to allowing piracy. Price discrimination allows the firm to exploit any network benefits from spreading use of their product while also raising revenue. In this sense, piracy is, at best, an inferior alternative to price discrimination. We also showed, even in the absence of price discrimination, that piracy provides a very ‘blunt instrument’ to expand the user base. Piracy may be profitable, but if it is profit maximizing to allow any customer to pirate then it is also profitable to allow all other similar customers to pirate. In this sense, piracy is more like an organized product ‘give-way’ aimed at buyers with a low intrinsic value for the product. There is no non-trivial piracy in the sense that some low value consumers purchase and others pirate. Our results show that the claims for profitable piracy based on the feedback between user-base and paying customers must be carefully examined. The underlying logic behind such claims of profitable piracy is simply the logic of price discrimination. Unless there is a reason to believe that potential pirates will systematically value a product less than other buyers and that there are relatively few pirates, then allowing IP rights to be degraded will not be in a firm’s interest. Our analysis has focused on one of the arguments for profitable piracy. As mentioned in the introduction, alternative arguments have been presented in the literature based on dynamic firm pricing and strategic interactions. Our model has also highlighted alternative ways in which a firm might be forced to exploit piracy to raise profits. In particular, if a seller is ‘stuck’ in equilibrium were no-one buys the product because of a rational fear of a low user base, allowing piracy might be a way to ‘break’ this equilibrium. While the resulting outcome for the seller will not be a global profit-maximizing equilibrium (of the type considered above) it will be better than equilibrium where no-one buys the product. The potential for such suboptimal equilibria and the role of allowing piracy to avoid such outcomes is an avenue for future research.