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«Vincent Mak v.mak Judge Business School, University of Cambridge, Trumpington Street, Cambridge CB2 1AG, United Kingdom Rami Zwick ...»

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“Pay what you want” as a profitable pricing strategy:

Theory and experimental evidence

Vincent Mak

v.mak@jbs.cam.ac.uk, Judge Business School, University of Cambridge, Trumpington Street,

Cambridge CB2 1AG, United Kingdom

Rami Zwick

rami.zwick@ucr.edu, Department of Management and Marketing, A. Gary Anderson Graduate

School of Management, University of California, Riverside, Riverside CA 92521

Akshay R. Rao

arao@umn.edu, Department of Marketing & Logistics Management, Carlson School of Management, University of Minnesota, May 8, 2010 The authors would like to acknowledge the comments of Tony Cui, George John, Amnon Rapoport, as well as seminar participants at the University of California, Berkeley, the University of California, Riverside, and the University of Cambridge, on earlier versions of this manuscript.

“Pay what you want” as a profitable pricing strategy:

Theory and experimental evidence Abstract Prevailing wisdom in the literature suggests that the success of a “pay what you want” (PWYW) pricing strategy depends on consumers’ altruistic inclinations, sense of fair play, or consumers’ willingness to reciprocate the firm’s generous offer. In this article, we consider whether PWYW can be profitable when the consumer’s only motive is self-interest. Through analyzing an infinitely repeated pricing game between a firm and a fixed consumer population, we find that PWYW could be as profitable as a fixed price regime, if the firm’s strategy is to threaten to switch to the fixed price regime over a length of time in the future, should PWYW not yield enough profits. If consumers are forward looking and there exist a sufficient number of consumers who find the firm’s fixed price regime to be more costly than other alternatives, then such a threat could lead to a sustainable PWYW regime. We also examine coordination mechanisms that may enhance the sustainability of this regime in practice, and present a laboratory study that provides support for some of our conclusions.

Keywords: Pay what you want; pay as you wish; participative pricing; experimental economics;

game theory.


1. Introduction In late 2007, the British band Radiohead launched their new album In Rainbows with an unusual strategy: customers could download the album from a specially created website and pay any price they wanted. If they so desired, they could pay nothing. This “pay what you want” (PWYW) campaign ran from October 10 to December 10, 2007. It generated considerable commentary in the music industry, including skepticism regarding its financial viability1. For, if consumers were allowed to download the new album for free, wouldn’t they all do just that?

Indeed, it was later estimated that about 62% of downloads of In Rainbows in October 2007 were free downloads, but a remarkable 38% of downloads were accompanied by a payment that averaged roughly $6.002 (Elberse and Bergsman 2008). Since there was no revenue sharing with record companies and retailers, the entire revenue accrued to the band, leading one band member to observe that in terms of digital income they “made more money out of this record than out of all the other Radiohead albums put together” (Thom Yorke, quoted in Wired magazine, issue 16.01, January 2008).

More recently (October 2009), to celebrate their one year anniversary, the developers of the indie video game “World of Goo” ran an experiment for one week, during which buyers could pay what they wished for the game whose list price was $20. During the first week of the experiment, about 57,000 people downloaded the game from the website and the average price paid for the game was $2.03. The developers declared the results a “huge success” and extended 1 Fortune Magazine listed Radiohead’s PWYW strategy among the “101 Dumbest Moments in Business” in 2007 (http://money.cnn.com/galleries/2007/fortune/0712/gallery.101_dumbest.fortune/59.html).

2 The average payment is a misleading statistic in this case. Jane Dyball, Warner Chappell’s Head of Business Affairs, the publishing company that licensed all digital rights on behalf of Radiohead, pointed out that the band and their management never announced a timeline for their PWYW experiment and were watching the average price daily with a view to potentially withdrawing it any moment should it drop too low. Dyball pointed out that the average price went down after the download moved from uberfans to less committed fans, as expected (http://musically.com/blog/2008/10/15/exclusive-warner-chappell-reveals-radioheads-in-rainbows-pot-of-gold/).

2 the experiment for another week3. The success declaration should be evaluated with respect to the reported 90% piracy rate for the game. Following the success of “World of Goo”, the developer of Crayon Physics Deluxe allowed consumers to pay as they wished for the game for one week (January 8-15, 2010). During this week 31,332 downloaded the game and paid on average $1.90, leading the developer to announce that the experiment was “way more popular” than he expected4.

Such PWYW pricing strategies are neither new nor rare, and are prevalent in a variety of contexts. Public radio and television stations in the United States employ membership drives for donations that contain all the essential features of a PWYW strategy. Many museums do not charge admission fees, but suggest to patrons that they donate whatever they want, and restaurants in the U.S., U.K., Australia and Spain have experimented with PWYW options on their menus (Gregory 2009). As a consequence, PWYW has recently begun to attract thoughtful academic scrutiny (e.g. Kim et al. 2009, Regner and Barria 2009, Gautier and van der Klaauw 2010, Gneezy et al. 2010, Chen et al. 2010). Many arguments for the successful employment of a PWYW strategy can be proffered. One class of arguments relies on revenue generation through consumers’ “social preferences”, which include their sense of altruism and fair play as well as their willingness to reciprocate the firm’s generous offer. Another argument is based on the notion of “loss leadership” and the generation of secondary income through an increased customer base and through cross selling. Musicians, for example, can gain publicity by giving away albums, which then leads to enhanced concert ticket sales and merchandizing; museums may generate traffic through free admissions and subsequently earn revenues through sales at their gift shops and cafeterias. However, such derivative income may not always be essential for

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PWYW to be successful. Consider Wikipedia’s attempts to generate donations at the end of 2008, when a banner with a “Donate Now” button appeared at the top of every Wikipedia page; the campaign eventually achieved its target of raising $6 million, and there was no secondary income associated with the strategy (Hughes 2009).

Our study examines whether PWYW strategies can successfully be employed when arguments based on social preferences and loss leadership are not operative. Specifically, if a firm is faced with purely self-interested consumers, and there are no secondary benefits, can PWYW still be a profitable pricing strategy relative to fixed pricing (FP)? We answer this question through a game-theoretic model as well as laboratory experimentation, and identify conditions under which PWYW is more beneficial than FP to both the firm and to consumers.

The principal intuition underlying our results is captured in Wikipedia’s 2008 fundraising campaign. In that campaign, Wikipedia underscored the argument that user donations “will help keep Wikipedia free”, and hinted that a failure to raise sufficient funds would lead to Wikipedia users being charged a subscription fee, or Wikipedia being forced to carry advertisements (Hughes 2009). In essence, sufficient donations would sustain Wikipedia’s PWYW model in the future, but if donations did not reach sufficiency, Wikipedia might begin to charge users a subscription fee that would potentially be higher than the donation solicited, or Wikipedia might entertain advertisements, an action that could reduce users’ future benefits because Wikipedia might no longer be truly neutral.5 In our model, we


the essential features of the strategy just described and investigate when it is incentive compatible for consumers. Consumers may be willing to pay a positive 5 The indie music download site Marathon of Dope, which operates on a PWYW basis, voices a plea of a similar nature in its web pages (e.g. http://marathonofdope.com/?p=634): “Whatever money you decide is reasonable to pay for the music at Marathon Of Dope will go directly to the artists. That money will enable them to continue making high caliber music and bring it directly to you.” The implicit threat to listeners is that insufficient current donations will force the artists to compromise on quality and efficient distribution of their music in the future.

4 amount under PWYW if the alternative they face is a relatively high fixed price. That is, if the firm’s willingness to switch to a high fixed price for a pre-specified length of time (which we call “punishment periods”) is a credible threat, then consumers have an incentive to pay a positive amount in the current period. This argument stands if every individual consumer’s timediscounted total expected utility gain under PWYW is at least as high as the corresponding total utility gain that she would enjoy if she paid nothing in the current period under PWYW and then paid fixed prices throughout the punishment periods. Our major theoretical results consist of a statement of this intuition in quantitative terms. Formally, we examine a class of simple firm

strategies in the following form in the context of infinitely repeated firm-consumers interactions:

(1) the firm continues to implement PWYW if total payment from consumers is not lower than a pre-announced threshold; (2) if the threshold is not reached in a particular period, the firm implements FP for a pre-specified number of periods from the next period onwards, before reverting to PWYW. Given this firm strategy, we find conditions under which a PWYWsustaining equilibrium exists on the consumers’ side, which generates higher profit than under FP. In other words, we identify parametric conditions that admit a PWYW equilibrium which is more profitable to the firm and more beneficial to consumers, than if the firm practices FP.

However, our equilibrium solutions are sensitive to coordination failures, because, given a threshold profit and a punishment strategy that fulfill the theoretical conditions, there is typically a great multitude of consumer-side equilibria, which makes it potentially difficult for consumers to align their behavior with respect to one particular equilibrium. Thus, we suggest four mechanisms that can be adopted by the firm to enhance consumer coordination. The functions of two of these mechanisms – payment constraints and probabilistic punishment – can be

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consumers are allowed to communicate with each other, and that consumers are provided suggested payments, are behavioral strategies inspired by previous literature, and require empirical verification. Therefore we report a laboratory experiment designed to understand: (a) whether (i) consumer communication and (ii) suggested payment enable subjects to sustain a theoretically admissible PWYW equilibrium; (b) as control conditions, whether (i) theoretically admissible PWYW equilibria are sustainable without coordination mechanisms, and (ii) whether PWYW is sustainable even when theory does not admit any PWYW equilibria. We conclude our paper with a discussion of the theoretical insights we obtain and their relevance to practitioners.

2. Literature and Model In this section, we first offer a brief review of the literature that is relevant to the PWYW phenomenon. We then present an analytical model that captures our core argument that selfinterested consumers might, under certain conditions, sustain a PWYW strategy that is profitable for the firm.

2.1 Related Literature While the literature on pricing strategies is voluminous, the literature that speaks to the PWYW pricing strategy is relatively sparse. One approach examines the secondary benefits that might accrue to the firm if PWYW strategies are employed. For instance, the viability of PWYW in the context of museum admissions has been studied empirically by Steiner (1997) and Toepler (2006). Steiner (1997) examines whether free admission can serve as a loss leader that increases overall museum revenues through souvenir sales and cafeteria sales, but finds empirically that

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admission typically do not donate as much as the amount recommended by the museum establishment. Seemingly, the recommended amount serves as a reference point, and consumers discount from that reference point (Rao and Sieben 1992).

A number of recent field studies on PWYW, including Kim et al. (2009), Regner and Barria (2009), Gautier and van der Klaauw (2010), and Gneezy et al. (2010) find that consumers often pay positive amounts, and identify factors that affect their payments. Kim et al. (2009) observe that social preferences such as altruism and a sense of fair play influence the amounts paid.

Regner and Barria (2009) suggest that consumers’ motivation to reciprocate the firm’s offer to allow comprehensive pre-purchase sampling (if there is such an offer) influences their PWYW payment positively. Gautier and van der Klaauw (2009), meanwhile, demonstrate that consumers who were told they could pay what they wanted after committing to a purchase on average paid more than those who were told they could pay what they wanted before committing to a purchase.

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