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Isomorphic Strategy Spaces in Game Theory

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  • Gagen, Michael

Abstract

This book summarizes ongoing research introducing probability space isomorphic mappings into the strategy spaces of game theory. This approach is motivated by discrepancies between probability theory and game theory when applied to the same strategic situation. In particular, probability theory and game theory can disagree on calculated values of the Fisher information, the log likelihood function, entropy gradients, the rank and Jacobian of variable transforms, and even the dimensionality and volume of the underlying probability parameter spaces. These differences arise as probability theory employs structure preserving isomorphic mappings when constructing strategy spaces to analyze games. In contrast, game theory uses weaker mappings which change some of the properties of the underlying probability distributions within the mixed strategy space. Here, we explore how using strong isomorphic mappings to define game strategy spaces can alter rational outcomes in simple games . Specific example games considered are the chain store paradox, the trust game, the ultimatum game, the public goods game, the centipede game, and the iterated prisoner's dilemma. In general, our approach provides rational outcomes which are consistent with observed human play and might thereby resolve some of the paradoxes of game theory.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 46176.

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Date of creation: 10 Apr 2013
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Handle: RePEc:pra:mprapa:46176

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Keywords: non-cooperative game theory; isomorphic probability spaces;

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  1. S. Huck & J. Oechssler, 1996. "The Indirect Evolutionary Approach To Explaining Fair Allocations," SFB 373 Discussion Papers 1996,13, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. AUMANN, Robert J., . "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP -167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Robert Evans & Jonathan P. Thomas, 1997. "Reputation and Experimentation in Repeated Games with Two Long-Run Players," Econometrica, Econometric Society, vol. 65(5), pages 1153-1174, September.
  4. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
  5. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
  6. Ernst Fehr & Simon Gaechter, . "Cooperation and Punishment in Public Goods Experiments," IEW - Working Papers 010, Institute for Empirical Research in Economics - University of Zurich.
  7. Robert Slonim & Alvin E. Roth, 1998. "Learning in High Stakes Ultimatum Games: An Experiment in the Slovak Republic," Econometrica, Econometric Society, vol. 66(3), pages 569-596, May.
  8. Fehr, Ernst & Schmidt, Klaus M., 1999. "A theory of fairness, competition, and cooperation," Munich Reprints in Economics 20650, University of Munich, Department of Economics.
  9. Ruffle, Bradley J., 1998. "More Is Better, But Fair Is Fair: Tipping in Dictator and Ultimatum Games," Games and Economic Behavior, Elsevier, vol. 23(2), pages 247-265, May.
  10. Lisa Cameron, 1995. "Raising the Stakes in the Ultimatum Game: Experimental Evidence From Indonesia," Working Papers 724, Princeton University, Department of Economics, Industrial Relations Section..
  11. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
  12. Axel Ockenfels & Gary E. Bolton, 2000. "ERC: A Theory of Equity, Reciprocity, and Competition," American Economic Review, American Economic Association, vol. 90(1), pages 166-193, March.
  13. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
  14. Aumann, Robert J., 1996. "Reply to Binmore," Games and Economic Behavior, Elsevier, vol. 17(1), pages 138-146, November.
  15. Paul Milgrom & John Roberts, 1997. "Predation, reputation , and entry deterrence," Levine's Working Paper Archive 1460, David K. Levine.
  16. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  17. Gary E Bolton & Rami Zuwick, 2010. "Anonymity versus punishments in ultimatum bargaining," Levine's Working Paper Archive 826, David K. Levine.
  18. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-36, July.
  19. Hessel Oosterbeek & Randolph Sloof & Gijs van de Kuilen, 2004. "Cultural differences in ultimatum game experiments: Evidence from a meta-analysis," Experimental 0401003, EconWPA.
  20. Nick Feltovich & John Duffy, 1999. "Does observation of others affect learning in strategic environments? An experimental study," International Journal of Game Theory, Springer, vol. 28(1), pages 131-152.
  21. Binmore, Ken, 1988. "Modeling Rational Players: Part II," Economics and Philosophy, Cambridge University Press, vol. 4(01), pages 9-55, April.
  22. Ochs, Jack & Roth, Alvin E, 1989. "An Experimental Study of Sequential Bargaining," American Economic Review, American Economic Association, vol. 79(3), pages 355-84, June.
  23. A. Meltzer & Peter Ordeshook & Thomas Romer, 1982. "Introduction," Public Choice, Springer, vol. 39(1), pages 1-3, January.
  24. Ernst Fehr & Urs Fischbacher, 2004. "Social norms and human cooperation," Macroeconomics 0409026, EconWPA.
  25. Thaler, Richard H, 1988. "The Ultimatum Game," Journal of Economic Perspectives, American Economic Association, vol. 2(4), pages 195-206, Fall.
  26. M. Rabin, 2001. "Incorporating Fairness into Game Theory and Economics," Levine's Working Paper Archive 511, David K. Levine.
  27. Hoffman, Elizabeth & McCabe, Kevin A & Smith, Vernon L, 1996. "On Expectations and the Monetary Stakes in Ultimatum Games," International Journal of Game Theory, Springer, vol. 25(3), pages 289-301.
  28. Binmore, K & Shaked, A & Sutton, J, 1985. "Testing Noncooperative Bargaining Theory: A Preliminary Study," American Economic Review, American Economic Association, vol. 75(5), pages 1178-80, December.
  29. Prasnikar, Vesna & Roth, Alvin E, 1992. "Considerations of Fairness and Strategy: Experimental Data from Sequential Games," The Quarterly Journal of Economics, MIT Press, vol. 107(3), pages 865-88, August.
  30. Burnell, Stephen J. & Evans, Lewis & Yao, Shuntian, 1999. "The Ultimatum Game: Optimal Strategies without Fairness," Games and Economic Behavior, Elsevier, vol. 26(2), pages 221-252, January.
  31. Hoffman Elizabeth & McCabe Kevin & Shachat Keith & Smith Vernon, 1994. "Preferences, Property Rights, and Anonymity in Bargaining Games," Games and Economic Behavior, Elsevier, vol. 7(3), pages 346-380, November.
  32. Kagel, John H. & Kim, Chung & Moser, Donald, 1996. "Fairness in Ultimatum Games with Asymmetric Information and Asymmetric Payoffs," Games and Economic Behavior, Elsevier, vol. 13(1), pages 100-110, March.
  33. Ebbe Groes & Hans JÛrgen Jacobsen & Birgitte Sloth, 1999. "Adaptive learning in extensive form games and sequential equilibrium," Economic Theory, Springer, vol. 13(1), pages 125-142.
  34. Loewenstein, George, et al, 1993. "Self-Serving Assessments of Fairness and Pretrial Bargaining," The Journal of Legal Studies, University of Chicago Press, vol. 22(1), pages 135-59, January.
  35. Joseph Henrich, 2000. "Does culture matter in economic behavior? Ultimatum game bargaining among the machiguenga," Artefactual Field Experiments 00067, The Field Experiments Website.
  36. Cooper, Russell & DeJong, Douglas V. & Forsythe, Robert & Ross, Thomas W., 1996. "Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games," Games and Economic Behavior, Elsevier, vol. 12(2), pages 187-218, February.
  37. Croson, Rachel T. A., 2000. "Thinking like a game theorist: factors affecting the frequency of equilibrium play," Journal of Economic Behavior & Organization, Elsevier, vol. 41(3), pages 299-314, March.
  38. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
  39. G. Bolton, 2010. "A comparative model of bargaining: theory and evidence," Levine's Working Paper Archive 263, David K. Levine.
  40. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
  41. Georg Kirchsteiger, 1994. "The role of envy in ultimatum games," ULB Institutional Repository 2013/5925, ULB -- Universite Libre de Bruxelles.
  42. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(02), pages 179-214, October.
  43. Binmore, Ken, 1996. "A Note on Backward Induction," Games and Economic Behavior, Elsevier, vol. 17(1), pages 135-137, November.
  44. Ariel Rubinstein, 1997. "Finite automata play the repeated prisioners dilemma," Levine's Working Paper Archive 1639, David K. Levine.
  45. Joseph Henrich, 2000. "Does Culture Matter in Economic Behavior? Ultimatum Game Bargaining among the Machiguenga of the Peruvian Amazon," American Economic Review, American Economic Association, vol. 90(4), pages 973-979, September.
  46. Abraham Neyman, 1999. "Cooperation in Repeated Games when the Number of Stages is Not Commonly Known," Econometrica, Econometric Society, vol. 67(1), pages 45-64, January.
  47. Douglas D. Davis & Charles A. Holt, 1999. "Equilibrium cooperation in two-stage games: Experimental evidence," International Journal of Game Theory, Springer, vol. 28(1), pages 89-109.
  48. Vriend, Nicolaas J., 1997. "Will reasoning improve learning?," Economics Letters, Elsevier, vol. 55(1), pages 9-18, August.
  49. Forsythe Robert & Horowitz Joel L. & Savin N. E. & Sefton Martin, 1994. "Fairness in Simple Bargaining Experiments," Games and Economic Behavior, Elsevier, vol. 6(3), pages 347-369, May.
  50. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May.
  51. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  52. Horst Raff & David Schmidt, 2000. "Cumbersome coordination in repeated games," International Journal of Game Theory, Springer, vol. 29(1), pages 101-118.
  53. Hart, Sergiu, 1992. "Games in extensive and strategic forms," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 2, pages 19-40 Elsevier.
  54. Sarin, Rajiv, 1999. "Simple play in the Prisoner's Dilemma," Journal of Economic Behavior & Organization, Elsevier, vol. 40(1), pages 105-113, September.
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