Do firms always benefit from the presence of active customers?

ABSTRACT

We study price personalization in a two period duopoly with horizontally differentiated products. In the second period, a firm has collected detailed information on its old customers, using it to engage in price personalization. Customers, when returning to buy, may choose to incur a cost in order to access the standard offer of their previous provider in addition to its personalized offer and the standard offer of its rival. The analysis confirms that firms’ second period profits are boosted when consumers are active in this sense (being equal to perfect price discrimination ones when initial market hares do not differ too much) but it reveals that this advantage is dissipated and possibly over-dissipated by the resulting fierce first-period competition for the market. Two-period aggregate profits are smaller with active customers provided the consumers are naive and/or the firms patient enough. Consumers’ access to both personalized and standard firms’ offers which benefit the oligopolists in mature markets may plausibly hurt them in emergent ones. The equilibrium is shown not to depend on the level of the cost as long as it is below some critical value.

KEYWORDS:

• Behavior-Base price discrimination
• active customers
• identity management

JEL CLASSIFICATION:

• D43, L13

Acknowledgement

Didier Laussel gratefully acknowledges support by the French National Research Agency Grant ANR-17-EURE-0020, and by the Excellence Initiative of Aix-Marseille University - A*MIDEX”.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ See for instance Max Freedman “How Businesses Are Collecting Data (And What They’re Doing With It)”, June 17, 2020, https://www.businessnewsdaily.com/10625-businesses-collecting-data.html.

² See for instance https://www.forrester.com/report/Chief+Data+ Officers+Evolve+Your+Teams+To+Accelerate+Impact+From+Data+Insights/-/E-RES163256#.

³ See Ezrachi and Stucke (2016). Mohammed (2017), Wallheimer (2018)., Mikians et al. (2012), (Mikians et al. 2013). See also Shaw and Vulkan (2012) for an empirical investigation.

⁴ https://www.nytimes.com/1990/12/13/us/white-men-get-better-deals-on-cars-study-finds.html?pagewanted=all.

⁵ Prices may be more or less finely targeted (See Liu and Serfes 2004) with in the limit fully personalized prices.

⁶ See Acquisti, 2008.

⁷ Chen, Choe, and Matsushima (2020) call this cost a privacy cost. We can more generally speak of an “access cost”.

⁸ This is the case when every consumer is recognized and receives a personalized offer by one or the other firm.

⁹ In their framework, the “targeted” consumers of a firm are the consumers whose it knows the exact preferences.

¹⁰ There are some, inessential, modelling differences however, since we use a standard Hotelling model with quadratic transportation costs whereas they use the “brand loyalty” model of Fudenberg and Tirole (2000).

¹¹ It is not necessary for this result that each firm be informed on the preferences of all customers as it is assumed by Thisse and Vives.

¹² See the survey by Acquisti, Taylor, and Wagman (2016), on the economics of privacy.

¹³ In the monopoly case see Belleflamme and Vergote (2016).

¹⁴ The market is not necessarily covered and segments may also possibly overlap.

¹⁵ A related paper is Belleflamme, Lam, and Vergote (2020). In an extension of their paper they consider the case when the firm must publish their uniform price, something akin to “ex-post price discrimination”. This is however different from the present paper since buying at the uniform price does not follow from customers’ choices and is free.

¹⁶ They take it equal to the value which ensures that a non-discriminating monopolist would just cover the market.

¹⁷ The same equilibrium obtains whether transportation costs are linear or quadratic.

¹⁸ Notice that given Assumption 1, this equation has one and only solution $\in \left[0,1\right].$ Moreover it is easy to check that $\underset{\_}{z}<1/4;$.

¹⁹ This gives rise to a competition dampening effect which partially compensates the effect of the decrease of second period profits on two-period ones.

²⁰ On the latter issue see for instance Gabszewicz, Laussel, and Sonnac (2005).

²¹ This effect appears since second-period profits are strictly increasing in the firm’s market share.

²² $\beta$ does not play any role in our model.

²³ In the case when the initial market shares are not too different.

²⁴ For the case of $z$ not too far from 1/2.

²⁵ The argument used in the proof in Proposition 1 for ruling out a price $p_1$ such Firm 1 poaches Firm 2’s consumers and does not offer personalized prices may be transposed for the case where Firm 1 commits not to use personalized prices (while Firm 2 does not make such commitment).

²⁶ Notice that, denoting $f(z)=(v-c-t)-t{z}^2+2tz,f(z)$ is maximum at $z=1$ and given Assumption 2, we have $f(0)>0$ and $f(1)>0$. It follows that $f(z)>0$ over [0, 1].

²⁷ Notice that $\underset{\_}{z}<1/4$ given Assumption 1.

²⁸ S stands for small, B for big.

²⁹ The main model is easily solved in this case, leaving qualitatively unchanged the equilibrium properties. Results are available on demand.

³⁰ The proof is only slightly different.

³¹ The argument is basically the same as in the proof of Lemma 2.

Additional information

Funding

The work was supported by the French National Research Agency [Grant ANR-17-EURE-0020].