Beyond Nash Equilibrium: Solution Concepts for the 21st Century

  • Joseph Y. Halpern
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7037)


An often useful way to think of security is as a game between an adversary and the “good” participants in the protocol. Game theorists try to understand games in terms of solution concepts; essentially, this is a rule for predicting how the game will be played. The most commonly used solution concept in game theory is Nash equilibrium. Intuitively, a Nash equilibrium is a strategy profile (a collection of strategies, one for each player in the game) such that no player can do better by deviating. The intuition behind Nash equilibrium is that it represent a possible steady state of play. It is a fixed point where each player holds correct beliefs about what other players are doing, and plays a best response to those beliefs. Part of what makes Nash equilibrium so attractive is that in games where each player has only finitely many possible deterministic strategies, and we allow mixed (i.e., randomized) strategies, there is guaranteed to be a Nash equilibrium [11] (this was, in fact, the key result of Nash’s thesis).


Nash Equilibrium Game Theory Multiagent System Solution Concept Sequential Equilibrium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abraham, I., Dolev, D., Gonen, R., Halpern, J.Y.: Distributed computing meets game theory: robust mechanisms for rational secret sharing and multiparty computation. In: Proc. 25th ACM Symposium on Principles of Distributed Computing, pp. 53–62 (2006)Google Scholar
  2. 2.
    Abraham, I., Dolev, D., Halpern, J.Y.: Lower Bounds on Implementing Robust and Resilient Mediators. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 302–319. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty processor. Journal of the ACM 32(2), 374–382 (1985)CrossRefzbMATHGoogle Scholar
  4. 4.
    Fudenberg, D., Tirole, J.: Game Theory. MIT Press, Cambridge (1991)zbMATHGoogle Scholar
  5. 5.
    Halpern, J.Y.: Beyond Nash Equilibrium: solution concepts for the 21st century. Lectures in Game Theory for Computer Scientists, pp. 264–289. Cambridge University Press, Cambridge (2011); an earlier version of the paper can be found in the Proceedings of Twenty-Seventh Annual ACM Symposium on Principles of Distributed Computing, pp. 1–10 (2008) and the Proceedings of the Eleventh International Conference on Principles of Knowledge Representation and Reasoning (KR 2008), pp. 6–14 (2008)CrossRefGoogle Scholar
  6. 6.
    Halpern, J.Y., Pass, R.: Iterated regret minimization: A more realistic solution concept. In: Proc. Twentieth International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 153–158 (2007); a longer version of the paper, with the title Iterated regret minimization: a new solution concept, will appear in Games and Economic BehaviorGoogle Scholar
  7. 7.
    Halpern, J.Y., Pass, R.: Game theory with costly computation. In: Proc. First Symposium on Innovations in Computer Science (2010)Google Scholar
  8. 8.
    Halpern, J.Y., Pass, R.: I don’t want to think about it now: Decision theory with costly computation. In: Principles of Knowledge Representation and Reasoning: Proc. Twelfth International Conference, KR 2010 (2010)Google Scholar
  9. 9.
    Halpern, J.Y., Rêgo, L.C.: Extensive games with possibly unaware players. In: Proc. Fifth International Joint Conference on Autonomous Agents and Multiagent Systems, pp. 744–751 (2006), full version available at
  10. 10.
    Kreps, D.M.: Game Theory and Economic Modeling. Oxford University Press, Oxford (1990)CrossRefGoogle Scholar
  11. 11.
    Nash, J.: Equilibrium points in n-person games. Proc. National Academy of Sciences 36, 48–49 (1950)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Osborne, M.J., Rubinstein, A.: A Course in Game Theory. MIT Press, Cambridge (1994)zbMATHGoogle Scholar
  13. 13.
    Pease, M., Shostak, R., Lamport, L.: Reaching agreement in the presence of faults. Journal of the ACM 27(2), 228–234 (1980)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Joseph Y. Halpern
    • 1
  1. 1.Computer Science DepartmentCornell UniversityIthacaUSA

Personalised recommendations