Document Open Access Logo

Price of Anarchy for Mechanisms with Risk-Averse Agents

Authors Thomas Kesselheim, Bojana Kodric

Thumbnail PDF


  • Filesize: 476 kB
  • 14 pages

Document Identifiers

Author Details

Thomas Kesselheim
  • University of Bonn, Institute of Computer Science, Bonn, Germany
Bojana Kodric
  • MPI for Informatics and Saarland University, Saarbrücken, Germany

Cite AsGet BibTex

Thomas Kesselheim and Bojana Kodric. Price of Anarchy for Mechanisms with Risk-Averse Agents. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 155:1-155:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


We study the price of anarchy of mechanisms in the presence of risk-averse agents. Previous work has focused on agents with quasilinear utilities, possibly with a budget. Our model subsumes this as a special case but also captures that agents might be less sensitive to payments than in the risk-neutral model. We show that many positive price-of-anarchy results proved in the smoothness framework continue to hold in the more general risk-averse setting. A sufficient condition is that agents can never end up with negative quasilinear utility after playing an undominated strategy. This is true, e.g., for first-price and second-price auctions. For all-pay auctions, similar results do not hold: We show that there are Bayes-Nash equilibria with arbitrarily bad social welfare compared to the optimum.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic mechanism design
  • Theory of computation → Quality of equilibria
  • Mechanism Design
  • Price of Anarchy
  • Risk Aversion
  • Smoothness


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Daniel Bernoulli. Exposition of a new theory on the measurement of risk. Commentaries of the Imperial Academy of Science of Saint Petersburg, 1738. Republished Econometrica 22(1), 23-36 (1954). Google Scholar
  2. Anand Bhalgat, Tanmoy Chakraborty, and Sanjeev Khanna. Mechanism design for a risk averse seller. In Proc. 8th Intl. Workshop Internet &Network Economics (WINE), pages 198-211, 2012. Google Scholar
  3. Shaddin Dughmi and Yuval Peres. Mechanisms for risk averse agents, without loss. CoRR, abs/1206.2957, 2012. Google Scholar
  4. Paul Dütting, Thomas Kesselheim, and Éva Tardos. Mechanism with unique learnable equilibria. In Proc. 15th Conf. Econom. Comput. (EC), pages 877-894, 2014. Google Scholar
  5. Amos Fiat and Christos H. Papadimitriou. When the players are not expectation maximizers. In Proc. 3rd Intl. Symp. Algorithmic Game Theory (SAGT), pages 1-14, 2010. Google Scholar
  6. Gadi Fibich, Arieh Gavious, and Aner Sela. All-pay auctions with risk-averse players. Int. J. Game Theory, 34(4):583-599, 2006. Google Scholar
  7. Hu Fu, Jason Hartline, and Darrell Hoy. Prior-independent auctions for risk-averse agents. In Proc. 14th Conf. Electr. Commerce (EC), pages 471-488. ACM, 2013. Google Scholar
  8. Martin Hoefer, Thomas Kesselheim, and Berthold Vöcking. Truthfulness and stochastic dominance with monetary transfers. ACM Trans. Econom. Comput., 4(2):11:1-11:18, 2016. Google Scholar
  9. Darrell Hoy. The concavity of atomic splittable congestion games with non-linear utility functions. In EC 2012, Workshop on Risk Aversion in Algorithmic Game Theory and Mechanism Design, 2012. Google Scholar
  10. Darrell Hoy, Nicole Immorlica, and Brendan Lucier. On-demand or spot? selling the cloud to risk-averse customers. In Proc. 12th Intl. Conf. Web and Internet Economics (WINE), pages 73-86, 2016. Google Scholar
  11. Audrey Hu, Steven A Matthews, and Liang Zou. Risk aversion and optimal reserve prices in first-and second-price auctions. J. Econom. Theory, 145(3):1188-1202, 2010. Google Scholar
  12. Thomas Kesselheim and Bojana Kodric. Price of anarchy for mechanisms with risk-averse agents. CoRR, abs/1804.09468, 2018. URL:
  13. Bettina S Klose and Paul Schweinzer. Auctioning risk: The all-pay auction under mean-variance preferences. Technical report, University of Zurich, 2014. URL:
  14. Harry M Markowitz. Portfolio selection: efficient diversification of investments, volume 16. Yale university press, 1968. Google Scholar
  15. Harry M. Markowitz. Mean-variance approximations to expected utility. Europ. J. Oper. Res., 234(2):346-355, 2014. Google Scholar
  16. Andreu Mas-Colell, Michael Dennis Whinston, Jerry R Green, et al. Microeconomic theory, volume 1. Oxford university press New York, 1995. Google Scholar
  17. Eric Maskin and John Riley. Optimal auctions with risk averse buyers. Econometrica, pages 1473-1518, 1984. Google Scholar
  18. Timothy Mathews and Brett Katzman. The role of varying risk attitudes in an auction with a buyout option. J. Econom. Theory, 27(3):597-613, 2006. Google Scholar
  19. Steven A Matthews. Selling to risk averse buyers with unobservable tastes. J. Econom. Theory, 30(2):370-400, 1983. Google Scholar
  20. Reshef Meir and David C. Parkes. Playing the wrong game: Smoothness bounds for congestion games with behavioral biases. SIGMETRICS Performance Evaluation Review, 43(3):67-70, 2015. Google Scholar
  21. Evdokia Nikolova and Nicolás E. Stier Moses. A mean-risk model for the traffic assignment problem with stochastic travel times. Oper. Res., 62(2):366-382, 2014. Google Scholar
  22. Evdokia Nikolova and Nicolás E. Stier Moses. The burden of risk aversion in mean-risk selfish routing. In Proc. 16th Conf. Econom. Comput. (EC), pages 489-506, 2015. Google Scholar
  23. Georgios Piliouras, Evdokia Nikolova, and Jeff S. Shamma. Risk sensitivity of price of anarchy under uncertainty. ACM Trans. Econom. Comput., 5(1):5:1-5:27, 2016. Google Scholar
  24. Tim Roughgarden. Intrinsic robustness of the price of anarchy. In Proc. 41st Symp. Theory of Computing (STOC), pages 513-522, 2009. Google Scholar
  25. Mukund Sundararajan and Qiqi Yan. Robust mechanisms for risk-averse sellers. In Proc. 11th Conf. Econom. Comput. (EC), pages 139-148, 2010. Google Scholar
  26. Vasilis Syrgkanis and Éva Tardos. Composable and efficient mechanisms. In Proc. 45th Symp. Theory of Computing (STOC), pages 211-220, 2013. Google Scholar
  27. John von Neumann and Oskar Morgenstern. Theory of games and economic behavior. Princeton, New Jersey: Princeton University Press. XVIII, 625 p., 1944. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail