Advertisement

Existence of Risk Strategy Equilibrium in Games Having No Pure Strategy Nash Equilibrium

  • Ka-man Lam
  • Ho-Fung Leung
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5044)

Abstract

Two key properties defining an intelligent agent are reactive and pro-active. Before designing an intelligent agent for any multi-agent system, we need to first understand how agents should behave and interact in that particular application, which can be done by modelling the application as a game. To analyze these games and to understand how decision-makers interact, we can use a collection of analytical tools known as Game Theory. Risk strategies is a new kind of game-theoretic strategy. Simulations in previous work have shown that agents using risk strategies are reactive as well as pro-active and thus have better performance than agents using other models or strategies in various applications. However, research on risk strategies has been focusing on formalization, application, and games having pure strategy Nash equilibrium. In this paper, we analyze a game having no pure strategy Nash equilibrium. We find that risk strategy equilibrium may exist even the game does not have pure strategy Nash equilibrium. We then summarize general conditions for the existence of risk strategy equilibrium. Simulation shows that agents using risk strategies also have better performance than agents using other existing strategies in a game having no pure strategy Nash equilibrium.

Keywords

Multiagent System Pure Strategy Intelligent Agent Risk Attitude Pareto Optimum 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Allais, M.: Le comportement de l’homme rationnel devant le risque: 367 critique des postulats et axiomes de l’ecole americaine. Econometrica 21, 503–546 (1953)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Aumann, R.J., Shapley, L.S.: Long-term competition - a game-theoretic analysis. In: Essays in Game Theory, pp. 1–15. Springer, New York (1994)CrossRefGoogle Scholar
  3. 3.
    Bernoulli, D.: Exposition of a new theory on the measurement of risk. Econometrica 22(1), 23–36 (1954)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    The Prisoner’s Dilemma Competition (2005), http://www.prisoners-dilemma.com/
  5. 5.
    Glass, A., Grosz, B.: Socially conscious decision-making. In: Proceedings of the Fourth International Conference on Autonomous Agents, pp. 217–224 (2000)Google Scholar
  6. 6.
    Kahneman, D., Tversky, A.: Prospect theory: An analysis of decision under risk. Econometrica 47(2), 263–291 (1979)CrossRefzbMATHGoogle Scholar
  7. 7.
    Lam, K.M., Leung, H.F.: Behavioral predictors and adaptive strategy for minority games. Physica A (submitted)Google Scholar
  8. 8.
    Lam, K.M., Leung, H.F.: Risk strategies and risk strategy equilibrium in agent interactions modeled as normal repeated 2 by 2 risk games. In: The Eighth Pacific Rim International Workshop on Multi-Agents (2005)Google Scholar
  9. 9.
    Lam, K.M., Leung, H.F.: Expected utility maximization and attractiveness maximization. In: Shi, Z.-Z., Sadananda, R. (eds.) PRIMA 2006. LNCS, vol. 4088, pp. 638–643. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Lam, K.M., Leung, H.F.: Formalizing risk strategies and risk strategy equilibrium in agent interactions modeled as infinitely repeated games. In: Shi, Z.-Z., Sadananda, R. (eds.) PRIMA 2006. LNCS, vol. 4088, pp. 138–149. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Lam, K.M., Leung, H.F.: A trust/honesty model with adaptive strategy for multiagent semi-competitive environments. Autonomous Agents and Multi-Agent Systems 120(3), 293–359 (2006)CrossRefGoogle Scholar
  12. 12.
    Lam, K.M., Leung, H.F.: An adaptive strategy for minority games. In: The 6th International Joint Conference on Autonomous Agents and Multiagent Systems (2007)Google Scholar
  13. 13.
    Lam, K.M., Leung, H.F.: An adaptive strategy for resource allocation modeled as minority game. In: The First IEEE International Conference on Self-Adaptive and Self-Organizing Systems, pp. 193–202 (2007)Google Scholar
  14. 14.
    Lam, K.M., Leung, H.F.: Incorporating risk attitude and reputation into infinitely repeated games and an analysis on the iterated prisoner’s dilemma. In: The 19th IEEE International Conference on Tools with Artificial Intelligence (2007)Google Scholar
  15. 15.
    Mui, L., Mohtashemi, M., Halberstadt, A.: A computational model of trust and reputation. In: Proceedings of 35th Hawaii International Conference on System Science (2002)Google Scholar
  16. 16.
    Osborne, M.J., Rubinstein, A.: A Course in Game Theory. MIT Press, Cambridge (1994)zbMATHGoogle Scholar
  17. 17.
    Rubiera, J.C., Lopez, J.M.M., Muro, J.D.: A fuzzy model of reputation in multi-agent systems. In: Proceedings of the Fifth International Conference on Autonomous Agents, pp. 25–26 (2001)Google Scholar
  18. 18.
    Rubinstein, A.: Equilibrium in supergames. In: Essays in Game Theory, pp. 17–27. Springer, New York (1994)CrossRefGoogle Scholar
  19. 19.
    Sartain, A.Q., North, A.J., Strange, J.R., Chapman, H.M.: Psychology – Understanding Human Behavior. McGraw-Hill Book Company, New York (1962)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Ka-man Lam
    • 1
  • Ho-Fung Leung
    • 1
  1. 1.Department of Computer Science and EngineeringThe Chinese University of Hong KongHong Kong

Personalised recommendations