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Price of Anarchy for Mechanisms with Risk-Averse Agents

Authors Thomas Kesselheim, Bojana Kodric

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Author Details

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

Funding

This work is supported by DFG through Cluster of Excellence MMCI.

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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) https://doi.org/10.4230/LIPIcs.ICALP.2018.155

Abstract

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
Keywords
  • Mechanism Design
  • Price of Anarchy
  • Risk Aversion
  • Smoothness

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