PRIVACY AND PRICE DISCRIMINATION

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units of the same good and the private information does not affect the relative advantage of each firm but, instead, it determines the number of units that he/

she is willing to buy. This model behaves similarly to the monopoly case and price discrimination benefits firms but harms consumers.¹²

of 1 and provides incentives for all consumers to reveal their willingness to pay for any positive amount

r

. Thus, the monopolist will maximize profits by lowering this payment to essentially 0.

The previous example illustrates a situation in which consumers cannot take advantage of the control over their information. Along the same line Belleflamme and Vergote (2016) shows that the access to a technology that prevents firms from learning about consumer preferences can be detrimental to their own welfare. A discussed earlier, in that model, the monopolist tracks consumers with a certain probability and, when successful, it offers a price equal to their valuation. Otherwise, they receive a generic price. This difference spurs consumers with a high valuation to acquire a hiding technology (e.g., software that eliminates cookies and erases their browsing history), since this helps them to have access to the generic price. The monopolist anticipates this behavior and, in order to discourage it, raises the generic price which makes the hiding technology useless for a larger proportion of the consumers, harming those that could never be identified. As a result, the quantity sold decreases, reducing total surplus. Consumers might be worse off overall, since those using the tracking technology may pay a lower price but a large proportion of consumers face a higher price.

The common message from these models is that, although individually consumers benefit from not disclosing information over their preferences, the impact of the strategies used to prevent the firm from learning on the final price may be self-defeating.

This negative effect extends to dynamic settings in which consumers make repeated purchasing decisions over time and firms learn from these choices about their willingness to pay. When consumers are aware of that effect they might modify strategically their purchasing decision in order to pretend that they have a lower valuation. These actions are very similar to the acquisition of a hiding technology since they will only be used by those consumers that have a high valuation. Similarly to what occurred in the models discussed earlier, when firms anticipate this behavior they will increase their future prices and harm consumers.

To illustrate this point, consider the two-period model discussed in Acquisti and Varian (2005). In that model a seller can set the price for the good in two periods. A unique consumer has a valuation constant over time that can be either high,

v

H, or low,

v

L, with probability

p

^{and 1 –}

p

, respectively. Because consumer valuation is constant the monopolist can use the initial period price to learn about the valuation and condition the second period price on that behavior. In order to analyze the effect of this strategy, assume first that the consumer is myopic. That is, he/she does not anticipate that the first purchasing decision can be used to extract surplus in the future once the valuation is known

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and he/she is offered a personalized price. As a result, if the probability that the consumer has a high valuation is sufficiently large, ₂

H

π >

−

L L

v

v v , it becomes optimal to charge a high price

p

1 =

v

H in the first period so that only a high-valuation consumer buys, uncovering this willingness to buy. The monopolist would then set a second period price equal to this consumer’s valuation, so that

p

2 =

v

_H

when the consumer bought in the first period and when he/she did not and, therefore the valuation was low, the price would be set to

p

2 =

v

_L.

Of course, a sophisticated consumer will anticipate this ruse. If the valuation is high, buying in the first period conveys information that leads to a high price in the second period. Pretending to be a low valuation consumer implies not buying in the first period in order to obtain a low price in the second. This mechanism is a reflection of the classical “ratchet effect” described in Freixas, Guesnerie and Tirole (1985). If the firm wants to prevent this misrepresentation from happening it will have to lower the first period price. Acquisti and Varian (2005) show that the profits from doing so are lower than those from giving up on price discrimination and charging either always a price equal to

v

L so that the consumer always buys or a price equal to

v

_H and exclude low valuation consumers.

Both scenarios are somehow extreme. When the monopolist faces a set of consumers, some of which are sophisticated and some are myopic, conditioning sales on post-purchasing decisions will typically be optimal (see also Taylor, 2004). Other reasons might also make this kind of strategy optimal. For example, products can be designed to fit certain consumer characteristics, learned from previous purchases. Consumers might then anticipate that the revelation of their valuation might entail a positive effect that could dominate the higher price that they will face.

Fudenberg and Tirole (2000) uncover another effect of conditioning on previous purchases. Contrary to the previous setup, they study a context of competition between two firms that offer differentiated products to the same consumers during two periods. These consumers have, as in the linear city, a preference for one of these products and they decide every period their purchasing decision. In second period, firms set a price for their product that they can condition on whether the agent is a returning consumer and he/she is, therefore, likely to have a high valuation for the good. As a result, in the second period the firm will charge a different price to loyal customers, that have indicated with their previous decision to have a high valuation for the good, and a low price to customers that it is aiming to poach from the other firm.

The authors show that this aggressive pricing strategy in the second period leads to inefficient switching. Consumers that preferred one of the products will be attracted to the competing firm because of the good deal that they are offered. This effect will feed back into higher prices in the first period, since each

firm anticipates that attracting consumers is less profitable than in the case in which the price could not depend on previous sales. The reason is that those consumers that have a weak preference for their product will be poached in the second period. As it turns out, the total welfare implications of this strategy are negative due to the misallocation of consumers among firms and the inefficient switching.

The previous discussion abstracts from the learning that may take place over time about consumer preferences and that we highlighted in previous sections. A firm will learn from consumers that bought in the first period and this information may allow future price discrimination. This feature is important because customer poaching is based on the fact that the firm that attracted the consumers in the first period cannot retain them by discounting the price in the future when the competitor is offering a better deal. With personalized prices this discount is possible without jeopardizing the profits from more loyal customers. Choe, King and Matsushima (2016) study such a model and show that as poaching becomes less effective, competition in the first period to attract customers becomes more intense, reducing initial prices.

Poaching can also be hindered when firms use the information they gather from their consumers in order to target additional services or taylor the products to their preferences, along the lines of the discussion in Varian (1997). Zhang (2011) discusses this issue by extending the model in Fudenberg and Tirole (2000) so that firms choose not only prices but also designs (or in the model, locations). While each firm offers a unique design in the first period, it may offer a second one to new customers in the second. When segmentation of the market is posible (that is, returning customers can be prevented from accessing the design aimed at new customers) it is optimal to offer two designs.

If segmentation is not feasible the offer of two designs is not an equilibrium since firms anticipate that it would lead to more competition and lower profits, for reasons that resemble those in Thisse and Vives (1988). Under segmentation each firm offers a second design that is closer to the preferences of the new customers, enticing their switching. Thus, in equilibrium customers with a weak preference for the product they bought in the first period switch to the other firm. However, contrary to Fudenberg and Tirole (2000), this switching is efficient since consumers buy a new design that is closer to their preferences than the original one.¹³

We finish this section by discussing how competition shapes the incentives for consumers to relinquish their privacy and provide information about their preferences beyond their previous purchases. Consider the case of a consumer

13 In this discussion, for the sake of simplicity, we have set the location of the original products to the extremes of the linear city. In the paper, however, this location or design is also endogenized and the author shows that, as a result, in the first period differentiation is reduced.

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who is uncertain about his/her most preferred product (e.g., a new smartphone) but can devote some time online to learn about the market offerings from existing retailers. Through his/her browsing history online sellers also learn about these preferences. The more time the consumer spends online the more precise will be the estimation that both the buyer and the sellers will have, improving the match between consumer preferences and an exiting product.

This kind of problem can be framed using the setup in Ganuza (2004). This paper considers a circular city in which N symmetric firms are located at the same distance from each other. Each location means a specialized design for the product. The consumer has standard preferences that linearly decay with the distance between his/her most preferred product and the location of the design chosen. The information gathered by the firm through the internet activity of the consumer translates into a public signal over the ideal product of this consumer.

The timing of the game is as follows. The consumer decides first on how much information to learn which then percolates to the firms in the market. The public signal is then realized and firms make offers on designs and prices to the consumer. The purchasing decision is made and payoffs are realized.

This model shows that the provision of information implies an interesting trade-off. As in models like Thisse and Vives (1988), the firm that has a design closest to the realization of the public signal will have an advantage over the competitors and will end up selling to the consumer. The other firms will price at marginal cost and the markup of the winner will be the difference in transportation costs between the closest design and the second closest one. The more time the consumer spends online and the more precise is the information revealed, the more aligned will be the purchasing decision with the ideal one, increasing efficiency. However, more information also grants more market power to the firm that has a design closest to the realized signal, increasing firm rents. These two forces create a trade-off. The intuition is the following. Suppose that there was no information. Both the consumer and all firms would behave as if the good was homogeneous since all products would have the same probability of being the most preferred one. In that case the price would equal marginal cost but the final allocation could be very inefficient. The probability of choosing the right design would be 1/N. Under perfect information the allocation is fully efficient and the closest firm has the largest competitive advantage. If the amount of information is somewhere in the middle and the second closest firm also has a significant chance of being the most preferred one, the difference in the expected utility of these designs would also be lower. Informational rents would also decrease in that case, alongside the efficiency in the allocation.

Finally, this trade-off changes with the number of firms. More competition reduces information rents and provides more scope for the consumer to find a

14 The Cambridge Analytica scandal, related to the US Presidential elections of 2016 and the Brexit vote, illustrates the reach of the information advantages that these platforms might grant beyond price discrimination. See https://www.nytimes.com/2018/04/04/us/politics/cambridge-analytica-scandal-fallout.

html for more information on the development of this scandal.

better match. As a result, the consumer decides to provide more information which increases social welfare. This conclusion is in contrast with the case in which there was a monopoly seller and consumers anticipated that the information provided would be used to extract rents from them. In other words, competition mitigates the privacy concerns of consumers.

In document ECONOMIC ANALYSIS OF THE DIGITAL REVO LUTIO N (página 135-140)