Privacy and Truthful Equilibrium Selection for Aggregative Games

  • Rachel Cummings
  • Michael Kearns
  • Aaron Roth
  • Zhiwei Steven Wu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9470)

Abstract

We study a very general class of games — multi-dimensional aggregative games — which in particular generalize both anonymous games and weighted congestion games. For any such game that is also large, we solve the equilibrium selection problem in a strong sense. In particular, we give an efficient weak mediator: a mechanism which has only the power to listen to reported types and provide non-binding suggested actions, such that (a) it is an asymptotic Nash equilibrium for every player to truthfully report their type to the mediator, and then follow its suggested action; and (b) that when players do so, they end up coordinating on a particular asymptotic pure strategy Nash equilibrium of the induced complete information game. In fact, truthful reporting is an ex-post Nash equilibrium of the mediated game, so our solution applies even in settings of incomplete information, and even when player types are arbitrary or worst-case (i.e. not drawn from a common prior). We achieve this by giving an efficient differentially private algorithm for computing a Nash equilibrium in such games. The rates of convergence to equilibrium in all of our results are inverse polynomial in the number of players n. We also apply our main results to a multi-dimensional market game.

Our results can be viewed as giving, for a rich class of games, a more robust version of the Revelation Principle, in that we work with weaker informational assumptions (no common prior), yet provide a stronger solution concept (ex-post Nash versus Bayes Nash equilibrium). In comparison to previous work, our main conceptual contribution is showing that weak mediators are a game theoretic object that exist in a wide variety of games – previously, they were only known to exist in traffic routing games. We also give the first weak mediator that can implement an equilibrium optimizing a linear objective function, rather than implementing a possibly worst-case Nash equilibrium.

Keywords

Differential privacy Equilibrium computation Mechanism design 

Notes

Acknowledgments

Research supported in part by NSF grants 1253345, 1101389, CNS-1254169, US-Israel Binational Science Foundation grant 2012348, Simons Foundation grant 361105, a Google Faculty Research Award, and the Alfred P. Sloan Foundation. Research performed while the first author was visiting the University of Pennsylvania.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Rachel Cummings
    • 1
  • Michael Kearns
    • 2
  • Aaron Roth
    • 2
  • Zhiwei Steven Wu
    • 2
  1. 1.Department of Computing and Mathematical SciencesCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Department of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA

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