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Pay-What-You-Want in Competition

  • Margaret Samahita EMAIL logo

Abstract

This paper presents an analysis of Pay-What-You-Want (PWYW) in competition which explains its entry and limited spread in the market. Sellers choose their pricing schemes sequentially while consumers share their surplus. The profitability and popularity of PWYW depend not only on consumers’ preferences, but also on market structure, product characteristics and sellers’ strategies. While there is no PWYW equilibrium, given a sufficiently high level of surplus-sharing and product differentiation, PWYW is chosen by later entrants to avoid Bertrand competition. The equilibrium results and their market characteristics are consistent with empirical examples of PWYW.

JEL Classification: D11; D21; L11

Funding statement: This work was supported by Jan Wallanders och Tom Hedelius Stiftelse samt Tore Browaldhs Stiftelse, Funder Id: http://dx.doi.org/10.13039/100007439, Grant Number: 2014-0041:1

Acknowledgements

I am grateful to Kjell Arne Brekke, Dirk Engelmann, Richard Friberg, Håkan J. Holm, Frederik Lundtofte, Alexander Sebald and participants at the 2014 ESA North American Meeting, the 3rd NYU Economics PhD Alumni Conference, the 2015 ESA World Meeting and the Microeconomics Seminar at Lund University for helpful comments and suggestions. Financial support from the Jan Wallander and Tom Hedelius Foundation is gratefully acknowledged.

Appendix

A Proofs

A.1 Proposition 1

πPWYW=(1θ)λc(k1)22kθc>c(k1)24k=πFP

implies

λ>(k1)2+4θk2(1θ)(k1)2=λˆ.

For existence of PWYW in equilibrium, it is easy to show that the set λˆ<1 is non-empty. It is also straightforward to derive the following:

dλˆdθ=(k+1)22(1θ)2(k1)2>0dλˆdk=2θ(k+1)(1θ)(k1)3<0.

A.2 Proposition 2

First note that whenever there are at least two FP sellers already in the market, the next entrant will always choose FP. With at least two FP sellers in the market, price equals marginal cost and fair buyers will always choose FP, resulting in the PWYW seller(s) incurring a loss from catering to the demand of free-riders. Hence for any subsequent entrant it is better to set a fixed price and get zero profit than choose PWYW and get negative profit. The same logic also applies whenever the current entrant anticipates that there would be at least two future FP sellers.

When there is one FP seller already in the market, if the next entrant chooses FP he would get zero profit from the price competition. If he chooses PWYW, his profit depends on λ.

  1. If λ<λ , PWYW profit is always negative whenever there is at least one FP competitor, regardless of what future entrants choose. Hence, he would rather choose FP himself than end up with a loss.

  2. If λ>λ , future entrants will also choose PWYW (that is, future entrants would avoid creating price competition with the other FP seller) since in a market with only 1 FP seller the PWYW sellers get positive profits:

    B=(1θ)λc(k1)28(n1)kθcn1>0.

    Hence he would choose PWYW.

  3. If λ=λ , and all subsequent entrants except the very last entrant choose PWYW, the very last entrant will randomize since B = 0. The positive probability that the very last entrant chooses FP will however yield negative expected profit for the second last entrant, who would then rather choose FP and be assured of a zero profit. All sellers will thus expect that in total there would be at least two FP sellers, and consequently no seller would risk choosing PWYW and having to serve only free-riders.

In short, when there is one FP seller already in the market, the next entrant will always choose FP except if λ>λ in which case all subsequent sellers will also choose PWYW.

Suppose now there is no FP seller currently in the market. The choice of the next entrant is as follows.

  1. If λ<λ , choosing FP will result in all subsequent sellers choosing FP as per the above, yielding zero profit. If he and all future entrants but the last one choose PWYW, the very last entrant would choose FP since being the only FP seller yields a higher profit than sharing the monopolist PWYW profit (since C > A). The second last mover will thus prefer to choose FP and get zero profit, since B < 0. Hence, by backward induction, since each seller anticipates there would be at least two subsequent FP sellers, any other previous seller will choose FP.

  2. If λ>λ , if he chooses FP he would be the only FP seller in the market since all subsequent entrants would prefer to earn positive PWYW profit (B > 0) than compete in price and earn zero profit. His own profit will thus be C, which is greater than any profit he could get as a PWYW seller. He will thus take the chance to be the only FP seller.

  3. If λ=λ , and all subsequent entrants but the very last one choose PWYW, the very last entrant will choose FP and be the only FP seller in the market earning C, while all previous PWYW entrants would earn B = 0. The second last entrant would thus rather choose FP, let the last entrant randomize, and earn an expected profit of C/2 . For the third last entrant, choosing PWYW earns him 0 at most. If he chooses FP and is the only FP seller in the market thus far, the next entrant will choose FP by the logic above while the last entrant will randomize. Thus, no matter the choice of the current seller, there will always be at least one future entrant choosing FP in addition to the probability 0.5 that the very last mover chooses FP. This means that the current seller will also prefer FP than risk negative expected profit from having to serve only free-riders.

In short, when there is no FP seller currently in the market, the next entrant will always choose FP.

It is easy to see that the arguments above hold for all n2 . Thus, the first mover will always choose FP. If λ>λ , the second mover will choose PWYW, which will be imitated by all subsequent movers. If λλ , the second and all subsequent movers will also choose FP. These results are summarized in Proposition 2.

For the existence of PWYW in equilibrium, it is easy to show that the set λ<1 is non-empty. It is also straightforward to derive the following:

dλdθ=8k(1θ)2(k1)2>0dλdk=8θ(k2+k1)(1θ)(k1)4<0.

A.3 Proposition 3

The game tree in Figure 5 captures the profit structure of the competition between there sellers with product differentiation. Define the following:

A=5λ(vc)12λ2(vc)24t
B=1tt6+λ(vc)22
C=5λ(vc)92λ2(vc)23t
D=1t2t9+λ(vc)32.
Figure 5: 
Competition between three sellers with product differentiation.
Figure 5:

Competition between three sellers with product differentiation.

First note that at C.1

λ(vc)3<B

unless

λ=t3(vc),

in which case

A=B=C=D=λ(vc)3=t9

and all sellers are indifferent between PWYW and FP.

At node C.4, the third mover will always choose FP unless C>t/9 or

t3(vc)<λ<t2(vc).

At nodes C.2 and C.3, the third mover will always choose FP unless A > D or t/(3(vc))<λ<16t/(39(vc)) .

All that remains is to check the choice of the second and first movers given the various regions for λ, yielding the equilibrium outcomes given in Proposition 3.

References

Chao, Y., J. Fernandez, and B. Nahata. 2015. “Pay-What-You-Want Pricing: Can It be Profitable?” Journal of Behavioral and Experimental Economics 57: 176–85.10.1016/j.socec.2014.09.004Search in Google Scholar

Chao, Y., J. Fernandez, and B. Nahata. 2017. “Pay-What-You-Want Pricing under Competition: Breaking the Bertrand Trap.” Working paper.10.2139/ssrn.3057674Search in Google Scholar

Chen, Y., O. Koenigsberg, and Z. J. Zhang. 2017. “Pay-as-You-Wish Pricing.” Marketing Science 36 (5): 780–91.10.1287/mksc.2017.1032Search in Google Scholar

Dana, J., R. A. Weber, and J. X. Kuang. 2007. “Exploiting Moral Wiggle Room: Experiments Demonstrating an Illusory Preference for Fairness.” Economic Theory 33 (1): 67–80.10.1007/s00199-006-0153-zSearch in Google Scholar

Economides, N. 1986. “Minimal and Maximal Product Differentiation in Hotelling’s Duopoly.” Economics Letters 21 (1): 67–71.10.1016/0165-1765(86)90124-2Search in Google Scholar

Fehr, E., G. Kirchsteiger, and A. Riedl. 1998. “Gift Exchange and Reciprocity in Competitive Experimental Markets.” European Economic Review 42 (1): 1–34.10.1016/S0014-2921(96)00051-7Search in Google Scholar

Fehr, E., and K. M. Schmidt. 1999. “A Theory of Fairness, Competition, and Cooperation.” Quarterly Journal of Economics 114 (3): 817–68.10.2307/j.ctvcm4j8j.14Search in Google Scholar

Fischbacher, U., S. Gächter, and E. Fehr. 2001. “Are People Conditionally Cooperative? Evidence from a Public Goods Experiment.” Economics Letters 71 (3): 397–404.10.1016/S0165-1765(01)00394-9Search in Google Scholar

Gächter, S., and B. Herrmann. 2009. “Reciprocity, Culture and Human Cooperation: Previous Insights and a New Cross-Cultural Experiment.” Philosophical Transactions of the Royal Society B: Biological Sciences 364 (1518): 791–806.10.1098/rstb.2008.0275Search in Google Scholar

Gautier, P. A., and B. van der Klaauw. 2012. “Selection in a Field Experiment with Voluntary Participation.” Journal of Applied Econometrics 27 (1): 63–84.10.1002/jae.1184Search in Google Scholar

Gerpott, T. 2017. “Pay-What-You-Want Pricing: An Integrative Review of the Empirical Research Literature.” Management Science Letters 7 (1): 35–62.10.5267/j.msl.2016.11.004Search in Google Scholar

Gneezy, A., U. Gneezy, G. Riener, and L. D. Nelson. 2012. “Pay-what-you-want, Identity, and Self-Signaling in Markets.” Proceedings of the National Academy of Sciences 109 (19): 7236–40.10.1073/pnas.1120893109Search in Google Scholar

Gravert, C. 2017. “Pride and Patronage – Pay-What-You-Want Pricing at a Charitable Bookstore.”Journal of Behavioral and Experimental Economics 67: 1–7.10.1016/j.socec.2017.01.009Search in Google Scholar

Greiff, M., and H. Egbert. 2018. “A Review of the Empirical Evidence on PWYW Pricing.” Economic and Business Review 20 (2): 169–93.10.15458/85451.64Search in Google Scholar

Greiff, M., H. Egbert, and K. Xhangolli. 2014. “Pay What You Want – but Pay Enough! Information Asymmetries and PWYW Pricing.” Management & Marketing. Challenges for the Knowledge Society 9 (2): 193–204.Search in Google Scholar

Herrmann, B., C. Thöni, and S. Gächter. 2008. “Antisocial Punishment Across Societies.” Science 319 (5868): 1362–67.10.1126/science.1153808Search in Google Scholar

Hoffman, E., K. McCabe, and V. L. Smith. 1996. “Social Distance and Other-Regarding Behavior in Dictator Games.” The American Economic Review 86 (3): 653–60.10.1017/CBO9780511528347.009Search in Google Scholar

Hotelling, H. 1929. “Stability in Competition.” Economic Journal 39 (153): 41–57.10.1007/978-1-4613-8905-7_4Search in Google Scholar

Isaac, R., J. Lightle, and D. Norton. 2015. “The Pay-What-You-Like Business Model: Warm Glow Revenues and Endogenous Price Discrimination.” Journal of Behavioral and Experimental Economics 57: 215–23.10.2139/ssrn.1612951Search in Google Scholar

Kahsay, G. A., and M. Samahita. 2015. “Pay-What-You-Want Pricing Schemes: A Self-Image Perspective.” Journal of Behavioral and Experimental Finance 7: 17–28.10.1016/j.jbef.2015.05.001Search in Google Scholar

Kim, J.-Y., M. Natter, and M. Spann. 2009. “Pay What You Want: A New Participative Pricing Mechanism.” Journal of Marketing 73 (1): 44–58.10.1509/jmkg.73.1.044Search in Google Scholar

Kim, J.-Y., M. Natter, and M. Spann. 2010. “Kish – Where Customers Pay as they Wish.” Review of Marketing Science 8 (2): 1–12.10.2202/1546-5616.1118Search in Google Scholar

Kocher, M. G., T. Cherry, S. Kroll, R. J. Netzer, and M. Sutter. 2008. “Conditional Cooperation on Three Continents.” Economics Letters 101 (3): 175–78.10.1016/j.econlet.2008.07.015Search in Google Scholar

Krämer, F., K. M. Schmidt, M. Spann, and L. Stich. 2017. “Delegating Pricing Power to Customers: Pay What You Want or Name Your Own Price?” Journal of Economic Behavior & Organization 136: 125–40.10.1016/j.jebo.2017.01.019Search in Google Scholar

Krzyżanowska, M., and J. Tkaczyk. 2016. “Pay-What-You-Want as a Participative Pricing Mechanism: Meta-Analysis of Development and Knowledge Dissemination.” International Journal of Management Cases 18 (2): 21–38.Search in Google Scholar

Kurzban, R., and D. Houser. 2005. “Experiments Investigating Cooperative Types in Humans: A Complement to Evolutionary Theory and Simulations.” Proceedings of the National Academy of Sciences 102 (5): 1803–07.10.1073/pnas.0408759102Search in Google Scholar

Mak, V., R. Zwick, A. R. Rao, and J. A. Pattaratanakun. 2015. “Pay What You Want” as a Threshold Public Good Provision.” Organizational Behavior and Human Decision Processes 127: 30–43.10.1016/j.obhdp.2014.11.004Search in Google Scholar

Natter, M., and K. Kaufmann. 2015. “Voluntary Market Payments: Underlying Motives, Success Drivers and Success Potentials.” Journal of Behavioral and Experimental Economics 57: 149–57.10.1016/j.socec.2015.05.008Search in Google Scholar

Park, S., S. Nam, and J. Lee. 2017. “Charitable Giving, Suggestion, and Learning from Others: Pay-What-You-Want Experiments at a Coffee Shop.” Journal of Behavioral and Experimental Economics 66: 16–22.10.1016/j.socec.2016.04.010Search in Google Scholar

Perloff, J. M., and S. C. Salop. 1985. “Equilibrium with Product Differentiation.” The Review of Economic Studies 52 (1): 107–20.10.2307/2297473Search in Google Scholar

Regner, T. 2015. “Why Consumers Pay Voluntarily: Evidence from Online Music.” Journal of Behavioral and Experimental Economics 57: 205–14.10.1016/j.socec.2014.10.006Search in Google Scholar

Regner, T., and J. A. Barria. 2009. “Do Consumers Pay Voluntarily? The Case of Online Music.” Journal of Economic Behavior & Organization 71 (2): 395–406.10.1016/j.jebo.2009.04.001Search in Google Scholar

Regner, T., and G. Riener. 2017. “Privacy Is Precious: On the Attempt of Lifting Anonymity on the Internet to Increase Revenue.” Journal of Economics & Management Strategy 26 (2): 318–36.10.1111/jems.12192Search in Google Scholar

Riener, G., and C. Traxler. 2012. “Norms, Moods, and Free Lunch: Longitudinal Evidence on Payments from a Pay-What-You-Want Restaurant.” The Journal of Socio-Economics 41 (4): 476–83.10.1016/j.socec.2011.07.003Search in Google Scholar

Schmidt, K., M. Spann, and R. Zeithammer. 2014. “Pay What You Want as a Marketing Strategy in Monopolistic and Competitive Markets.” Management Science 61(6): 1217–36.10.1287/mnsc.2014.1946Search in Google Scholar

Tudón, J. F. 2015. “Pay-What-You-Want because I Do Not Know How Much to Charge You.” Economics Letters 137: 41–44.10.1016/j.econlet.2015.10.021Search in Google Scholar

Published Online: 2019-06-08

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