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An Experiment on Forward vs. Backward Induction: How Fairness and Level k Reasoning Matter

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  • Balkenborg Dieter

    (The University of Exeter, Exete, United Kingdom of Great Britain and Northern Ireland)

  • Nagel Rosemarie

    (Universitat Pompeu Fabra, ICREA, BGSE, Barcelona, Spain)

Abstract

We report the experimental results on a game with an outside option where forward induction contradicts with backward induction based on a focal, risk dominant equilibrium. The latter procedure yields the equilibrium selected by Harsanyi and Selten’s (1988) theory, which is hence here in contradiction with strategic stability (Kohlberg and Mertens, 1986). We find the Harsanyi-Selten solution to be in much better agreement with our data. Since fairness and bounded rationality seem to matter we discuss whether recent behavioral theories, in particular fairness theories and learning, might explain our findings. The fairness theories by Bolton and Ockenfels (2000), Charness and Rabin (2002), or Fehr and Schmidt (1999), when calibrated using experimental data on dictator- and ultimatum games, indeed predict that forward induction should play no role for our experiment and that the outside option should be chosen by all sufficiently selfish players. However, there is a multiplicity of ‘fairness equilibria’, some of which seem to be rejected because they require too many levels of reasoning. We show that learning theories based on naive priors could alternatively explain our results, but not that of closely related experiments.

Suggested Citation

  • Balkenborg Dieter & Nagel Rosemarie, 2016. "An Experiment on Forward vs. Backward Induction: How Fairness and Level k Reasoning Matter," German Economic Review, De Gruyter, vol. 17(3), pages 378-408, August.
  • Handle: RePEc:bpj:germec:v:17:y:2016:i:3:p:378-408
    DOI: 10.1111/geer.12099
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    1. van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, vol. 48(2), pages 476-496, August.
    2. Gary Charness & Matthew Rabin, 2002. "Understanding Social Preferences with Simple Tests," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(3), pages 817-869.
    3. Huck, Steffen & Muller, Wieland, 2005. "Burning money and (pseudo) first-mover advantages: an experimental study on forward induction," Games and Economic Behavior, Elsevier, vol. 51(1), pages 109-127, April.
    4. Cooper, Russell & Douglas V. DeJong & Robert Forsythe & Thomas W. Ross, 1993. "Forward Induction in the Battle-of-the-Sexes Games," American Economic Review, American Economic Association, vol. 83(5), pages 1303-1316, December.
    5. Vincent P. Crawford & Uri Gneezy & Yuval Rottenstreich, 2008. "The Power of Focal Points Is Limited: Even Minute Payoff Asymmetry May Yield Large Coordination Failures," American Economic Review, American Economic Association, vol. 98(4), pages 1443-1458, September.
    6. Roberto Weber & Colin Camerer & Marc Knez, 2004. "Timing and Virtual Observability in Ultimatum Bargaining and “Weak Link” Coordination Games," Experimental Economics, Springer;Economic Science Association, vol. 7(1), pages 25-48, February.
    7. R. Muller & Asha Sadanand, 2003. "Order of Play, Forward Induction, and Presentation Effects in Two-Person Games," Experimental Economics, Springer;Economic Science Association, vol. 6(1), pages 5-25, June.
    8. Jordi Brandts & Gary Charness, 2011. "The strategy versus the direct-response method: a first survey of experimental comparisons," Experimental Economics, Springer;Economic Science Association, vol. 14(3), pages 375-398, September.
    9. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    10. Vincent P. Crawford & Miguel A. Costa-Gomes, 2006. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 96(5), pages 1737-1768, December.
    11. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 817-868.
    12. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    13. Stahl Dale O. & Wilson Paul W., 1995. "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 10(1), pages 218-254, July.
    14. Binmore, Ken & McCarthy, John & Ponti, Giovanni & Samuelson, Larry & Shaked, Avner, 2002. "A Backward Induction Experiment," Journal of Economic Theory, Elsevier, vol. 104(1), pages 48-88, May.
    15. Ken Binmore & Larry Samuelson, 1999. "Evolutionary Drift and Equilibrium Selection," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(2), pages 363-393.
    16. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    17. Armin Falk & Ernst Fehr & Urs Fischbacher, 2003. "On the Nature of Fair Behavior," Economic Inquiry, Western Economic Association International, vol. 41(1), pages 20-26, January.
    18. Mitzkewitz, Michael & Nagel, Rosemarie, 1993. "Experimental Results on Ultimatum Games with Incomplete Information," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(2), pages 171-198.
    19. Schotter Andrew & Weigelt Keith & Wilson Charles, 1994. "A Laboratory Investigation of Multiperson Rationality and Presentation Effects," Games and Economic Behavior, Elsevier, vol. 6(3), pages 445-468, May.
    20. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    21. 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.
    22. Binmore, Ken, 1988. "Modeling Rational Players: Part II," Economics and Philosophy, Cambridge University Press, vol. 4(1), pages 9-55, April.
    23. Brandts, Jordi & Holt, Charles A., 1995. "Limitations of dominance and forward induction: Experimental evidence," Economics Letters, Elsevier, vol. 49(4), pages 391-395, October.
    24. Balkenborg, Dieter & Schlag, Karl H., 2007. "On the evolutionary selection of sets of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 133(1), pages 295-315, March.
    25. Johnson, Eric J. & Camerer, Colin & Sen, Sankar & Rymon, Talia, 2002. "Detecting Failures of Backward Induction: Monitoring Information Search in Sequential Bargaining," Journal of Economic Theory, Elsevier, vol. 104(1), pages 16-47, May.
    26. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    27. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 9-41, June.
    28. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    29. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    30. Caminati, Mauro & Innocenti, Alessandro & Ricciuti, Roberto, 2006. "Drift effect under timing without observability: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 61(3), pages 393-414, November.
    31. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2013. "Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications," Journal of Economic Literature, American Economic Association, vol. 51(1), pages 5-62, March.
    32. Cooper, Russell & De Jong, Douglas V. & Forsythe, Robert & Ross, Thomas W., 1992. "Forward induction in coordination games," Economics Letters, Elsevier, vol. 40(2), pages 167-172, October.
    33. Brandts, Jordi & Holt, Charles A, 1993. "Adjustment Patterns and Equilibrium Selection in Experimental Signaling Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 279-302.
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