Advertisement

How to Play Well in Non-zero Sum Games: Some Lessons from Generalized Traveler’s Dilemma

  • Predrag T. Tošić
  • Philip Dasler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6890)

Abstract

We are interested in two-person games whose structure is far from zero-sum. We study the iterated Traveler’s Dilemma (TD) which is a two-player, non-zero sum game that, depending on the exact values of its critical parameters, may offer plenty of incentives for cooperation. We first briefly summarize the results of a round-robin tournament with 36 competing strategies that was motivated by the work by Axelrod et al. on the iterated Prisoner’s Dilemma. We then generalize the “default” version of Iterated TD with respect to two important game parameters, the bonus value and the “granularity” of the allowable bids. We analytically show the impact of the ratio of these two parameters on the game structure. Third, we re-run the 36-player round-robin tournament and investigate how varying the bonus-to-granularity ratio affects relative performances of various types of strategies in the tournament. We draw some conclusions based on those results and outline some promising ways forward in further investigating games whose structures seem to defy the prescriptions of classical game theory.

Keywords

Nash Equilibrium MultiAgent System Pure Strategy Dollar Amount Strategy Pair 
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.
    Axelrod, R.: Effective choice in the prisoner’s dilemma. Journal of Conflict Resolution 24(1), 3–25 (1980)Google Scholar
  2. 2.
    Axelrod, R.: The evolution of cooperation. Science 211(4489), 1390–1396 (1981)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Axelrod, R.: The evolution of cooperation. Basic Books (2006)Google Scholar
  4. 4.
    Basu, K.: The traveler’s dilemma. Scientific American Magazine (June 2007)Google Scholar
  5. 5.
    Basu, K.: The traveler’s dilemma: Paradoxes of rationality in game theory. The American Economic Review 84(2), 391–395 (1994)Google Scholar
  6. 6.
    Becker, T., Carter, M., Naeve, J.: Experts playing the traveler’s dilemma, Department of Economics, University of Hohenheim, Germany (January 2005)Google Scholar
  7. 7.
    Capra, C.M., Goeree, J.K., Gmez, R., Holt, C.A.: Anomalous behavior in a traveler’s dilemma? The American Economic Review 89(3), 678–690 (1999)CrossRefGoogle Scholar
  8. 8.
    Dasler, P., Tosic, P.: The iterated traveler’s dilemma: Finding good strategies in games with bad structure: Preliminary results and analysis. In: Proc of the 8th Euro. Workshop on Multi-Agent Systems, EUMAS 2010 (December 2010)Google Scholar
  9. 9.
    Dasler, P., Tosic, P.: Playing challenging iterated two-person games well: A case study on iterated travelers dilemma. In: Proc. of WorldComp. Foundations of Computer Science FCS 2011 (to appear, July 2011)Google Scholar
  10. 10.
    Goeree, J.K., Holt, C.A.: Ten little treasures of game theory and ten intuitive contradictions. The American Economic Review 91(5), 1402–1422 (2001)CrossRefGoogle Scholar
  11. 11.
    Land, S., van Neerbos, J., Havinga, T.: Analyzing the traveler’s dilemma Multi-Agent systems project (2008), http://www.ai.rug.nl/mas/finishedprojects/2008/JoelSanderTim/index.html
  12. 12.
    Littman, M.L.: Friend-or-Foe q-learning in General-Sum games. In: Proc. of the 18th Int’l Conf. on Machine Learning, pp. 322–328. Morgan Kaufmann Publishers Inc., San Francisco (2001)Google Scholar
  13. 13.
    Neumann, J.V., Morgenstern, O.: Theory of games and economic behavior. Princeton University Press, Princeton (1944)zbMATHGoogle Scholar
  14. 14.
    Osborne, M.: An introduction to game theory. Oxford University Press, New York (2004)Google Scholar
  15. 15.
    Pace, M.: How a genetic algorithm learns to play traveler’s dilemma by choosing dominated strategies to achieve greater payoffs. In: Proc. of the 5th International Conference on Computational Intelligence and Games, pp. 194–200 (2009)Google Scholar
  16. 16.
    Parsons, S., Wooldridge, M.: Game theory and decision theory in Multi-Agent systems. Autonomous Agents and Multi-Agent Systems 5, 243–254 (2002)CrossRefzbMATHGoogle Scholar
  17. 17.
    Rapoport, A., Chammah, A.M.: Prisoner’s Dilemma. Univ. of Michigan Press (December 1965)Google Scholar
  18. 18.
    Rosenschein, J.S., Zlotkin, G.: Rules of encounter: designing conventions for automated negotiation among computers. MIT Press, Cambridge (1994)Google Scholar
  19. 19.
    Watkins, C.: Learning from delayed rewards. Ph.D. thesis, University of London, King’s College (United Kingdom), England (1989)Google Scholar
  20. 20.
    Watkins, C., Dayan, P.: Q-learning. Machine Learning 8(3-4), 279–292 (1992)CrossRefzbMATHGoogle Scholar
  21. 21.
    Wooldridge, M.: An Introduction to MultiAgent Systems. John Wiley and Sons, Chichester (2009)Google Scholar
  22. 22.
    Zeuthen, F.F.: Problems of monopoly and economic warfare / by F. Zeuthen ; with a preface by Joseph A. Schumpeter. Routledge and K. Paul, London (1967); first published 1930 by George Routledge & Sons LtdGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Predrag T. Tošić
    • 1
  • Philip Dasler
    • 1
  1. 1.Department of Computer ScienceUniversity of HoustonHoustonUSA

Personalised recommendations