IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Isomorphic Strategy Spaces in Game Theory

  • Gagen, Michael

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: https://mpra.ub.uni-muenchen.de/46176/1/MPRA_paper_46176.pdf
File Function: original version
Download Restriction: no

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

as
in new window

Length:
Date of creation: 10 Apr 2013
Date of revision:
Handle: RePEc:pra:mprapa:46176
Contact details of provider: Postal:
Ludwigstraße 33, D-80539 Munich, Germany

Phone: +49-(0)89-2180-2459
Fax: +49-(0)89-2180-992459
Web page: https://mpra.ub.uni-muenchen.de

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Bolton Gary E. & Zwick Rami, 1995. "Anonymity versus Punishment in Ultimatum Bargaining," Games and Economic Behavior, Elsevier, vol. 10(1), pages 95-121, July.
  2. 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.
  3. Ernst Fehr & Urs Fischbacher, 2004. "Social norms and human cooperation," Macroeconomics 0409026, EconWPA.
  4. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
  5. V. Prasnikar & A. Roth, 1998. "Considerations of fairness and strategy: experimental data from sequential games," Levine's Working Paper Archive 451, David K. Levine.
  6. Bolton, Gary E, 1991. "A Comparative Model of Bargaining: Theory and Evidence," American Economic Review, American Economic Association, vol. 81(5), pages 1096-136, December.
  7. 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.
  8. Joseph Henrich, 2000. "Does culture matter in economic behavior? Ultimatum game bargaining among the machiguenga," Artefactual Field Experiments 00067, The Field Experiments Website.
  9. Georg Kirchsteiger, 1994. "The role of envy in ultimatum games," ULB Institutional Repository 2013/5925, ULB -- Universite Libre de Bruxelles.
  10. Evans, Lewis & Burnell, Stephen & Yao, Shuntian, 1999. "The Ultimatum Game: Optimal Strategies without Fairness," Working Paper Series 3939, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.
  11. Cooper, R. & DeJong, D.W. & Ross, T.W., 1992. "Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games," Papers 36, Boston University - Industry Studies Programme.
  12. N/A, 1996. "Note:," Foreign Trade Review, , vol. 31(1-2), pages 1-1, January.
  13. Sarin, Rajiv, 1999. "Simple play in the Prisoner's Dilemma," Journal of Economic Behavior & Organization, Elsevier, vol. 40(1), pages 105-113, September.
  14. Ebbe Groes & Hans JÛrgen Jacobsen & Birgitte Sloth, 1999. "Adaptive learning in extensive form games and sequential equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(1), pages 125-142.
  15. 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.
  16. 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.
  17. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 817-868.
  18. Ariel Rubinstein, 1997. "Finite automata play the repeated prisioners dilemma," Levine's Working Paper Archive 1639, David K. Levine.
  19. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  20. David Kreps & Paul Milgrom & John Roberts & Bob Wilson, 2010. "Rational Cooperation in the Finitely Repeated Prisoners' Dilemma," Levine's Working Paper Archive 239, David K. Levine.
  21. Hessel Oosterbeek & Randolph Sloof & Gijs van de Kuilen, 2004. "Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis," Experimental Economics, Springer, vol. 7(2), pages 171-188, 06.
  22. 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.
  23. Horst Raff & David Schmidt, 2000. "Cumbersome coordination in repeated games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 101-118.
  24. 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.
  25. Steffen Huck & Joerg Oechssler, 1995. "The Indirect Evolutionary Approach to Explaining Fair Allocations," Game Theory and Information 9507001, EconWPA, revised 27 Aug 1998.
  26. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
  27. M. Rabin, 2001. "Incorporating Fairness into Game Theory and Economics," Levine's Working Paper Archive 511, David K. Levine.
  28. Thaler, Richard H, 1988. "The Ultimatum Game," Journal of Economic Perspectives, American Economic Association, vol. 2(4), pages 195-206, Fall.
  29. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  30. Paul Milgrom & John Roberts, 1997. "Predation, reputation , and entry deterrence," Levine's Working Paper Archive 1460, David K. Levine.
  31. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-36, July.
  32. 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.
  33. 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.
  34. Simon Gachter & Ernst Fehr, 2000. "Cooperation and Punishment in Public Goods Experiments," American Economic Review, American Economic Association, vol. 90(4), pages 980-994, September.
  35. 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.
  36. Aumann, Robert J., 1996. "Reply to Binmore," Games and Economic Behavior, Elsevier, vol. 17(1), pages 138-146, November.
  37. Douglas D. Davis & Charles A. Holt, 1999. "Equilibrium cooperation in two-stage games: Experimental evidence," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 89-109.
  38. 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.
  39. 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.
  40. Hoffman, Elizabeth & McCabe, Kevin A & Smith, Vernon L, 1996. "On Expectations and the Monetary Stakes in Ultimatum Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(3), pages 289-301.
  41. 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.
  42. Nick Feltovich & John Duffy, 1999. "Does observation of others affect learning in strategic environments? An experimental study," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 131-152.
  43. Dufwenberg, Martin & Kirchsteiger, Georg, 2004. "A theory of sequential reciprocity," Games and Economic Behavior, Elsevier, vol. 47(2), pages 268-298, May.
  44. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
  45. 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.
  46. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(02), pages 179-214, October.
  47. Binmore, Ken, 1996. "A Note on Backward Induction," Games and Economic Behavior, Elsevier, vol. 17(1), pages 135-137, November.
  48. 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.
  49. Cameron, Lisa A, 1999. "Raising the Stakes in the Ultimatum Game: Experimental Evidence from Indonesia," Economic Inquiry, Western Economic Association International, vol. 37(1), pages 47-59, January.
  50. A. Meltzer & Peter Ordeshook & Thomas Romer, 1982. "Introduction," Public Choice, Springer, vol. 39(1), pages 1-3, January.
  51. Vriend, Nicolaas J., 1997. "Will reasoning improve learning?," Economics Letters, Elsevier, vol. 55(1), pages 9-18, August.
  52. 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.
  53. Binmore, Ken, 1988. "Modeling Rational Players: Part II," Economics and Philosophy, Cambridge University Press, vol. 4(01), pages 9-55, April.
  54. M. Ruth & K. Donaghy & P. Kirshen, 2006. "Introduction," Chapters, in: Regional Climate Change and Variability, chapter 1 Edward Elgar Publishing.
  55. 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.
  56. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  57. 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.
  58. 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.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:46176. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.