# Discriminatory auctions with resale

- 67 Downloads
- 1 Citations

## Abstract

We consider multi-unit discriminatory auctions where ex ante symmetric bidders have single-unit demands and resale is allowed after the bidding stage. When bidders use the optimal auction to sell items in the resale stage, the equilibrium in the auction without resale is no longer an equilibrium in an auction with resale. We find a symmetric and monotone equilibrium when there are two units for sale, and, interestingly, we show that there may not be a symmetric and monotone equilibrium if there are more than two units.

## Keywords

Multi-unit auctions Resale Discriminatory auctions Reserve price## JEL Classification

D44 C72## Notes

### Acknowledgements

We are very grateful and deeply indebted to Vijay Krishna for his contributions to an earlier version of this paper. We also thank Christoph Mueller and Gabor Virag for valuable discussion and anonymous reviewers for helpful comments.

## Supplementary material

## References

- Athey, S.: Single crossing properties and the existence of pure strategy equilibria in games of incomplete information. Econometrica
**69**(4), 861–889 (2001)Google Scholar - Ausubel, L.M., Cramton, P., Pycia, M., Rostek, M., Weretka, M.: Demand reduction and inefficiency in multi-unit auctions. Rev. Econ. Stud.
**81**(4), 1366–1400 (2014)Google Scholar - Bukhchandani, S., Huang, C.-F.: Auctions with resale markets: an exploratory model of treasury bill markets. Rev. Fin. Stud.es
**2**(3), 311–339 (1989)Google Scholar - Calzolari, G., Pavan, A.: Monopoly with resale. RAND J. Econ.
**37**(2), 362–375 (2006)Google Scholar - Cheng, H.: Auctions with resale and bargaining power. J. Math. Econ.
**47**(3), 300–308 (2011)Google Scholar - Cheng, H., Tan, G.: Asymmetric common-value auctions with applications to private-value auctions with resale. Econ. Theory
**45**(1–2), 253–290 (2010)Google Scholar - Dworczak, P.: The Effects of Post-Auction Bargaining between Bidders, Stanford University working paper (2015)Google Scholar
- Engelbrecht-Wiggans, R., Kahn, C.M.: Multi-unit auctions with uniform prices. Econ. Theory
**12**(2), 227–258 (1998a)Google Scholar - Engelbrecht-Wiggans, R., Kahn, C.M.: Multi-unit pay-your-bid auctions with variable awards. Games Econ. Behav.
**23**(1), 25–42 (1998b)Google Scholar - Filiz-Ozbay, E., Lopez-Vargas, K., Ozbay, E.Y.: Multi-object auctions with resale: theory and experiment. Games Econ. Behav.
**89**, 1–16 (2015)Google Scholar - Garratt, R.J., Troger, T., Zheng, C.Z.: Collusion via resale. Econometrica
**77**(4), 1095–1136 (2009)Google Scholar - Garratt, R., Troger, T.: Speculation in standard auctions with resale. Econometrica
**74**(3), 753–769 (2006)Google Scholar - Gupta, M., Lebrun, B.: First price auctions with resale. Econ. Lett.
**64**(2), 181–185 (1999)Google Scholar - Hafalir, I., Krishna, V.: Asymmetric auctions with resale. Am. Econ. Rev.
**98**(1), 87–112 (2008)Google Scholar - Hafalir, I., Krishna, V.: Revenue and efficiency effects of resale in first-price auctions. J. Math. Econ.
**45**(9–10), 589–602 (2009)Google Scholar - Haile, P.A.: Partial pooling at the reserve price in auctions with resale opportunities. Games Econ. Behav.
**33**(2), 231–248 (2000)Google Scholar - Haile, P.A.: Auctions with resale markets: an application to U.S. forest service timber sales. Am. Econ. Rev.
**91**(3), 399–427 (2001)Google Scholar - Haile, P.A.: Auctions with private uncertainty and resale opportunities. J. Econ. Theory
**108**(1), 72–110 (2003)Google Scholar - Krishna, V.: Auction Theory. Elsevier Science, Academic, San Diego (2002)Google Scholar
- Lebrun, B.: First-price auctions with resale and with outcomes robust to bid disclosure. RAND J. Econ.
**41**(1), 165–178 (2010)Google Scholar - McAdams, D.: Isotone equilibrium in games of incomplete information. Econometrica
**71**(4), 1191–1214 (2003)Google Scholar - Milgrom, P., Weber, R.J.: A theory of auctions and competitive bidding, ii. Econ. Theory Auct.
**2**, 179–194 (2000)Google Scholar - Noussair, C.: Equilibria in a multi-object uniform price sealed bid auction with multi-unit demands. Econ. Theory
**5**(2), 337–351 (1995)Google Scholar - Pagnozzi, M.: Bidding to lose? Auctions with resale. RAND J. Econ.
**38**(4), 1090–1112 (2007)Google Scholar - Pagnozzi, M.: Are speculators unwelcome in multi-object auctions? Am. Econ. J. Microecon.
**2**(2), 97–131 (2010)Google Scholar - Pagnozzi, M., Saral, K.J.: Multi-object Auctions with Resale: an Experimental Analysis. MPRA Paper 43665, University Library of Munich, Germany (2013)Google Scholar
- Reny, P.J.: On the existence of pure and mixed strategy nash equilibria in discontinuous games. Econometrica
**67**(5), 1029–1056 (1999)Google Scholar - Reny, P.J.: On the existence of monotone pure-strategy equilibria in Bayesian games. Econometrica
**79**(2), 499–553 (2011)Google Scholar - Saral, K.J.: Speculation and demand reduction in english clock auctions with resale. J. Econ. Behav. Org.
**84**(1), 416–431 (2012)Google Scholar - Virag, G.: First-price auctions with resale: the case of many bidders. Econ. Theory
**52**(1), 129–163 (2013)Google Scholar - Xu, X., Levin, D., Ye, L.: Auctions with entry and resale. Games Econ. Behav.
**79**, 92–105 (2013)Google Scholar - Zheng, C.Z.: Optimal auction with resale. Econometrica
**70**(6), 2197–2224 (2002)Google Scholar - Zheng, C.Z.: Existence of Monotone Equilibria in First-price Auctions with Resale. Working paper (2014)Google Scholar