# Entanglement Between Demand and Supply in Markets with Bandwagon Goods

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## Abstract

Whenever customers’ choices (e.g. to buy or not a given good) depend on others choices (cases coined ‘positive externalities’ or ‘bandwagon effect’ in the economic literature), the demand may be multiply valued: for a same posted price, there is either a small number of buyers, or a large one—in which case one says that the customers *coordinate*. This leads to a dilemma for the seller: should he sell at a high price, targeting a small number of buyers, or at low price targeting a large number of buyers? In this paper we show that the interaction between demand and supply is even more complex than expected, leading to what we call the *curse of coordination*: the pricing strategy for the seller which aimed at maximizing his profit corresponds to posting a price which, not only assumes that the customers will coordinate, but also lies very near the critical price value at which such high demand no more exists. This is obtained by the detailed mathematical analysis of a particular model formally related to the Random Field Ising Model and to a model introduced in social sciences by T.C. Schelling in the 70’s.

## Keywords

Choice under social influence Pricing RFIM Schelling## Notes

### Acknowledgements

We are grateful to David Martimort for helpful suggestions. We thank Annick Vignes for useful comments and for a critical reading of the manuscript. We gratefully acknowledge the anonymous referees for their comments.

## References

- 1.Schelling, T.C.: J. Math. Sociol.
**1**, 143 (1971) CrossRefGoogle Scholar - 2.Schelling, T.C.: J. Confl. Resolut.
**XVII**(3), 381–428 (1973) CrossRefGoogle Scholar - 3.Schelling, T.S.: Micromotives and Macrobehavior. Norton, New York (1978) Google Scholar
- 4.Arthur, W.B.: Am. Econ. Rev.
**84**, 406 (1994) Google Scholar - 5.Arthur, W.B.: Science
**284**, 107 (1999) ADSCrossRefGoogle Scholar - 6.Granovetter, M.: Am. J. Sociol.
**83**(6), 1360 (1978) Google Scholar - 7.Crane, J.: Am. J. Sociol.
**96**, 1226 (1991) CrossRefGoogle Scholar - 8.Durlauf, S.N.: J. Econ. Growth
**1**, 349 (1996) CrossRefGoogle Scholar - 9.Benabou, R.: Rev. Econ. Stud.
**63**, 237 (1996) zbMATHCrossRefGoogle Scholar - 10.Glaeser, E.L., Sacerdote, B., Scheinkman, J.A.: Q. J. Econ.
**CXI**, 507 (1996) CrossRefGoogle Scholar - 11.Ostrom, E.: J. Econ. Perspect.
**14**, 137 (2000) CrossRefGoogle Scholar - 12.Topa, G.: Rev. Econ. Stud.
**68**(2), 261 (2001) zbMATHCrossRefGoogle Scholar - 13.Conley, T., Topa, G.: J. Appl. Econom.
**17**(4), 303 (2002) CrossRefGoogle Scholar - 14.Ioannides, Y., Zabel, J.: J. Appl. Econom.
**18**, 563 (2003) CrossRefGoogle Scholar - 15.Durlauf, S.N.: In: Bowles, S., Durlauf, S.N., Hoff, K. (eds.) Poverty Traps. Princeton University Press, Princeton (2006) Google Scholar
- 16.Krauth, B.: Can. J. Econ.
**39**(2), 414 (2006) CrossRefGoogle Scholar - 17.Krauth, B.V.: J. Econom.
**133**(1), 243–271 (2006) MathSciNetCrossRefGoogle Scholar - 18.Soetevent, A., Kooreman, P.: J. Appl. Econ.
**22**(3), 599–624 (2007) MathSciNetCrossRefGoogle Scholar - 19.Artle, R., Averous, C.: Bell J. Econ. Manag. Sci.
**4**(1), 89 (1973) CrossRefGoogle Scholar - 20.Rohlfs, J.: Bell J. Econ. Manag. Sci.
**5**, 16 (1974) MathSciNetCrossRefGoogle Scholar - 21.Von Rabenau, B., Stahl, K.: Bell J. Econ. Manag. Sci.
**5**(2) 651 (1974) CrossRefGoogle Scholar - 22.Curien, N., Gensollen, M.: Rev. Econ.
**2**(mars), 203 (1987). Google Scholar - 23.Katz, M.L., Shapiro, C.: J. Econ. Perspect.
**8**(2), 93 (1994) CrossRefGoogle Scholar - 24.Shapiro, C., Varian, H.: Information Rules: A Strategic Guide to the Network Economy. Harvard Business School Press, Boston (1999) Google Scholar
- 25.Rohlfs, J.: Bandwagon Effects in High-Technology Industries. MIT Press, Cambridge (2001) Google Scholar
- 26.Leibenstein, H.: Q. J. Econ.
**64**(2), 183 (1950) CrossRefGoogle Scholar - 27.Granovetter, M., Soong, R.: J. Econ. Behav. Organ.
**7**, 83 (1986) CrossRefGoogle Scholar - 28.Becker, G.S., Murphy, K.: Social Economics. Market Behavior in a Social Environment. Belknap Press & Harvard University Press, Cambridge (2000) Google Scholar
- 29.Manski, C.F.: J. Econ. Perspect.
**14**(3), 115 (2000) CrossRefGoogle Scholar - 30.Durlauf, S.N.: In: Arthur, B., Durlauf, S.N., Lane, D. (eds.) The Economy as an Evolving Complex System II. Santa Fe Institute Studies in the Sciences of Complexity, vol. XVII, pp. 81–104. Addison-Wesley, Reading (1997) Google Scholar
- 31.Brock, W.A., Durlauf, S.N.: Rev. Econ. Stud.
**68**, 235 (2001) MathSciNetzbMATHCrossRefGoogle Scholar - 32.Nadal, J.P., Phan, D., Gordon, M.B., Vannimenus, J.: Quant. Finance
**5**(6), 557 (2005) MathSciNetzbMATHCrossRefGoogle Scholar - 33.Sethna, J.P.: Statistical Mechanics: Entropy, Order Parameters and Complexity. Oxford University Press, London (2006) zbMATHGoogle Scholar
- 34.Föllmer, H.: J. Math. Econ.
**1**(1), 51 (1974) zbMATHCrossRefGoogle Scholar - 35.Galam, S., Gefen, Y., Shapir, Y.: J. Math. Sociol.
**9**, 1 (1982) zbMATHCrossRefGoogle Scholar - 36.Orléan, A.: J. Econ. Behav. Organ.
**28**, 257 (1995) CrossRefGoogle Scholar - 37.Weisbuch, G., Stauffer, D.: Physica A
**323**, 651 (2003) MathSciNetADSzbMATHCrossRefGoogle Scholar - 38.Phan, D., Gordon, M.B., Nadal, J.P.: In: Bourgine, P., Nadal, J.-P. (eds.) Cognitive Economics, pp. 335–358. Springer, Berlin (2004) CrossRefGoogle Scholar
- 39.Bouchaud, J.P.: arXiv:1209.0453v1 (2012)
- 40.Gordon, M.B., Nadal, J.P., Phan, D., Semeshenko, V.: Math. Models Methods Appl. Sci.
**19**(Suppl. 1), 1441 (2009) MathSciNetzbMATHCrossRefGoogle Scholar - 41.Michard, Q., Bouchaud, J.P.: Eur. Phys. J., B Cond. Matter Phys.
**47**, 151 (2005) ADSGoogle Scholar - 42.Borghesi, C., Bouchaud, J.P.: Qual. Quant.
**41**(4), 557 (2007) CrossRefGoogle Scholar - 43.Semeshenko, V., Gordon, M.B., Nadal, J.P.: Physica A
**387**, 4903 (2008) ADSCrossRefGoogle Scholar - 44.Becker, G.S.: J. Polit. Econ.
**99**, 1109 (1991) CrossRefGoogle Scholar - 45.Gordon, M.B., Nadal, J.P., Phan, D., Vannimenus, J.: Physica A
**356**(2–4), 628 (2005) ADSCrossRefGoogle Scholar - 46.Cabral, L.M.B., Salant, D.J., Woroch, G.A.: Int. J. Ind. Organ.
**17**(2), 199 (1999) CrossRefGoogle Scholar - 47.Bansaid, B., Lesne, J.P.: Int. J. Ind. Organ.
**14**(6), 837 (1996) CrossRefGoogle Scholar - 48.Dechert, W.D., Brock, W.: In: Maler, K.-G., Perrings, C., Starrett, D. (eds.) Economic and Ecological Modelling. The Beijer Institute, The Royal Academy of Sciences, Stockholm (2000) Google Scholar