Optimal Mechanism Design with Risk-Loving Agents

  • Evdokia Nikolova
  • Emmanouil PountourakisEmail author
  • Ger Yang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11316)


One of the most celebrated results in mechanism design is Myerson’s characterization of the revenue optimal auction for selling a single item. However, this result relies heavily on the assumption that buyers are indifferent to risk. In this paper we investigate the case where the buyers are risk-loving, i.e. they prefer gambling to being rewarded deterministically. We use the standard model for risk from expected utility theory, where risk-loving behavior is represented by a convex utility function.

We focus our attention on the special case of exponential utility functions. We characterize the optimal auction and show that randomization can be used to extract more revenue than when buyers are risk-neutral. Most importantly, we show that the optimal auction is simple: the optimal revenue can be extracted using a randomized take-it-or-leave-it price for a single buyer and using a loser-pay auction, a variant of the all-pay auction, for multiple buyers. Finally, we show that these results no longer hold for convex utility functions beyond exponential.


  1. Cai, Y., Devanur, N.R., Weinberg, S.M.: A duality based unified approach to bayesian mechanism design. In: Proceedings of the Forty-eighth Annual ACM Symposium on Theory of Computing, pp. 926–939. ACM (2016)CrossRefGoogle Scholar
  2. Chawla, S., Goldner, K., Miller, J.B., Pountourakis, E.: Revenue maximization with an uncertainty-averse buyer. In: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 2050–2068. SIAM (2018)CrossRefGoogle Scholar
  3. Daskalakis, C., Deckelbaum, A., Tzamos, C.: Mechanism design via optimal transport. In: Proceedings of the Fourteenth ACM Conference on Electronic Commerce, pp. 269–286. ACM (2013)Google Scholar
  4. Daskalakis, C., Deckelbaum, A., Tzamos, C.: Strong duality for a multiple-good monopolist. Econometrica 85(3), 735–767 (2017)MathSciNetCrossRefGoogle Scholar
  5. Dughmi, S., Peres, Y.: Mechanisms for risk averse agents, without loss. arXiv preprint arXiv:1206.2957 (2012)
  6. Fu, H., Hartline, J., Hoy, D.: Prior-independent auctions for risk-averse agents. In: Proceedings of the Fourteenth ACM Conference on Electronic Commerce, pp. 471–488. ACM (2013)Google Scholar
  7. Giannakopoulos, Y., Koutsoupias, E.: Duality and optimality of auctions for uniform distributions. In: Proceedings of the Fifteenth ACM Conference on Economics and Computation, pp. 259–276. ACM (2014)Google Scholar
  8. Giannakopoulos, Y., Koutsoupias, E.: Selling two goods optimally. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 650–662. Springer, Heidelberg (2015). Scholar
  9. Hinnosaar, T.: On the impossibility of protecting risk-takers. Econ. J. (2017). ISSN 1468–0297CrossRefGoogle Scholar
  10. Li, J., et al.: Energy coupon: a mean field game perspective on demand response in smart grids. ACM SIGMETRICS Perform. Eval. Rev. 43(1), 455–456 (2015)CrossRefGoogle Scholar
  11. Lu, F.: Framework for a lottery-based incentive scheme and its influence on commuting behaviors: an MIT case study. PhD thesis, Massachusetts Institute of Technology (2015)Google Scholar
  12. Maskin, E., Riley, J.: Optimal auctions with risk averse buyers. Econ.: J. Econ. Soc. 52, 1473–1518 (1984)MathSciNetCrossRefGoogle Scholar
  13. Matthews, S.A.: Selling to risk averse buyers with unobservable tastes. J. Econ. Theory 30(2), 370–400 (1983)CrossRefGoogle Scholar
  14. Merugu, D., Prabhakar, B.S., Rama, N.S.: An incentive mechanism for decongesting the roads: a pilot program in Bangalore. In: Proceedings of ACM NetEcon Workshop. ACM (2009)Google Scholar
  15. Myerson, R.B.: Optimal auction design. Math. Oper. Res. 6(1), 58–73 (1981)MathSciNetCrossRefGoogle Scholar
  16. Nikolova, E., Pountourakis, E., Yang, G.: Optimal mechanism design with risk-loving agents. CoRR, abs/1810.02758 (2018).
  17. Pluntke, C., Prabhakar, B.: INSINC: a platform for managing peak demand in public transit. JOURNEYS Land Transp. Auth. Acad. Singap., 31–39 (2013)Google Scholar
  18. Von Neumann, J., Morgenstern, O.: Theory of games and economic behavior. Bull. Amer. Math. Soc 51(7), 498–504 (1945)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Evdokia Nikolova
    • 1
  • Emmanouil Pountourakis
    • 1
    Email author
  • Ger Yang
    • 1
  1. 1.The University of Texas at AustinAustinUSA

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