Advertisement

International Journal of Game Theory

, Volume 43, Issue 1, pp 65–88 | Cite as

Imperfect recall and time inconsistencies: an experimental test of the absentminded driver “paradox”

  • M. Vittoria Levati
  • Matthias Uhl
  • Ro’i Zultan
Article

Abstract

Absentmindedness is a special case of imperfect recall, in which a single history includes more than one decision node in an information set. Put differently, players, after making a decision, sometimes face it again without recalling having ‘been there before’. Piccione and Rubinstein (Game Econ Behav 20(1):3–24, 1997b) have argued that absentmindedness may lead to time inconsistencies. Specifically, in certain cases, a player’s optimal strategy as calculated when called to choose an action (the action stage) deviates from the optimal strategy as calculated in a preceding planning stage, although preferences remain constant and no new information is revealed between the two stages. An alternative approach assumes that the player maximizes expected payoff in the action stage while considering his actions at other decision nodes to be immutable. With this approach, no time inconsistencies arise. The present paper explores this issue from a behavioral point of view. We elicit participants’ strategies in an experimental game of absentmindedness, separately for a planning stage and an action stage. We find systematic and robust time inconsistencies under four variations of the experiment and using ten different parameterizations of the game. We conclude that real decisions under absentmindedness without commitment are susceptible to time inconsistencies.

Keywords

Imperfect recall Absentmindedness Dynamic inconsistency Experiment 

Notes

Acknowledgments

Financial support from the Max Planck Society is gratefully acknowledged. We thank the members and students of the Center for the Study of Rationality in Jerusalem and the Max Planck Institute of Economics in Jena, and particularly Bob Aumann, Ido Erev, Werner Güth, Joe Halpern, Sergiu Hart, Yaakov Kareev, Dave Lagnado, Motty Perry, Michele Piccione, Ariel Rubinstein, Larry Samuelson, Sudipta Sarangi, Ran Shorrer, and Shmuel Zamir for helpful discussions and comments. We thank Christoph Göring for assistance with programming.

Supplementary material

182_2013_373_MOESM1_ESM.pdf (107 kb)
Supplementary material 1 (pdf 106 KB)

References

  1. Abreu D, Rubinstein A (1988) The structure of Nash equilibrium in repeated games with finite automata. Econometrica 56(6):1259–1281CrossRefGoogle Scholar
  2. Aumann R, Hart S, Perry M (1997a) The absent-minded driver. Game Econ Behav 20:102–116CrossRefGoogle Scholar
  3. Aumann R, Hart S, Perry M (1997b) The forgetful passenger. Game Econ Behav 20(1):117–120CrossRefGoogle Scholar
  4. Bardsley N, Cubitt R, Loomes G, Moffatt P, Starmer C, Sugden R (2010) Experimental economics: rethinking the rules. Princeton University Press, PrincetonGoogle Scholar
  5. Battigalli P (1997) Dynamic consistency and imperfect recall. Game Econ Behav 20(1):31–50CrossRefGoogle Scholar
  6. Binmore K (1996) A note on imperfect recall. In: Albers W, Güth W, Hammerstein P, Moldovanu B, Van Damme E (eds) Understanding strategic interaction—essays in honor of Reinhard Selten. Springer, Berlin, pp 51–62Google Scholar
  7. Board O (2003) The not-so-absent-minded driver. Res Econ 57(3):189–200CrossRefGoogle Scholar
  8. Cowan N (2001) The magical number 4 in short-term memory: a reconsideration of mental storage capacity. Behav Brain Sci 24(1):87–114CrossRefGoogle Scholar
  9. Deck C, Sarangi S (2009) Inducing imperfect recall in the lab. J Econ Behav Organ 69:64–74CrossRefGoogle Scholar
  10. Deese J, Kaufman RA (1957) Serial effects in recall of unorganized and sequentially organized verbal material. J Exp Psychol 54(3):180–187CrossRefGoogle Scholar
  11. Elga A (2000) Self-locating belief and the sleeping beauty problem. Analysis 60(266):143–147CrossRefGoogle Scholar
  12. Epstein LG, Schmeidler D (2003) Recursive multiple-priors. J Econ Theory 113:1–31CrossRefGoogle Scholar
  13. Fischbacher U (2007) z-tree: Zurich toolbox for ready-made economic experiments. Exp Econ 10(2): 171–178Google Scholar
  14. Gilboa I (1997) A comment on the absent-minded driver paradox. Game Econ Behav 20(1):25–30CrossRefGoogle Scholar
  15. Gilboa I, Schmeidler D (1989) Maxmin expected utility with nonunique prior. J Math Econ 18:141–153CrossRefGoogle Scholar
  16. Greiner B (2004) An online recruitment system for economic experiments. In: Kremer K, Macho V (eds) Forschung und wissenschaftliches Rechnen 2003. GWDG Bericht 63, Gesellschaft für Wissenschaftliche Datenverarbeitung, Göttingen, pp 79–93Google Scholar
  17. Grove AJ, Halpern JY (1997) On the expected value of games with absentmindedness. Game Econ Behav 20(1):51–65CrossRefGoogle Scholar
  18. Halpern JY (1997) On ambiguities in the interpretation of game trees. Game Econ Behav 20(1):66–96CrossRefGoogle Scholar
  19. Hitchcock C (2004) Beauty and the bets. Synthese 139(3):405–420CrossRefGoogle Scholar
  20. Huck S, Müller W (2002) Absent-minded drivers in the lab: testing Gilboa’s model. Int Game Theory Rev 4(4):435–448CrossRefGoogle Scholar
  21. Isbell J (1957) Finitary games. In: Contributions to the theory of games III. Princeton University Press, Princeton, pp 79–96Google Scholar
  22. Kahneman D (1973) Attention and effort. Prentice Hall, Englewood CliffsGoogle Scholar
  23. Kahneman D (2011) Thinking: fast and slow. Farrar Straus and Giroux, New YorkGoogle Scholar
  24. Kahneman D, Tversky A (1979) Prospect theory: analysis of decision under risk. Econometrica 47(2): 263–292Google Scholar
  25. Kareev Y (2000) Seven (indeed, plus or minus two) and the detection of correlations. Psychol Rev 107(2):397–402CrossRefGoogle Scholar
  26. Kareev Y, Warglien M (2003) Cognitive overload and the evaluation of risky alternatives: the effects of sample size, information format and attitude to risk. Discussion Paper 340, Center for the Study of RationalityGoogle Scholar
  27. Kline J (2005) Imperfect recall and the relationships between solution concepts in extensive games. Econ Theory 25(3):703–710CrossRefGoogle Scholar
  28. Kuhn HW (1953) Extensive games and the problem of information. In: Contributions to the theory of games II. Princeton University Press, Princeton, pp 193–216Google Scholar
  29. Lehrer E (1988) Repeated games with stationary bounded recall strategies. J Econ Theory 46(1):130–144CrossRefGoogle Scholar
  30. Lipman BL (1997) More absentmindedness. Game Econ Behav 20(1):97–101CrossRefGoogle Scholar
  31. Miller GA (1956) The magic number 7, plus or minus 2: some limits on our capacity for processing information. Psychol Rev 63:81–97CrossRefGoogle Scholar
  32. Murdock BB Jr (1962) The serial position effect of free recall. J Exp Psychol 64(5):482–488CrossRefGoogle Scholar
  33. Piccione M, Rubinstein A (1997a) The absent-minded driver’s paradox: synthesis and responses. Game Econ Behav 20(1):121–130CrossRefGoogle Scholar
  34. Piccione M, Rubinstein A (1997b) On the interpretation of decision problems with imperfect recall. Game Econ Behav 20(1):3–24CrossRefGoogle Scholar
  35. Rubinstein A (1986) Finite automata play the repeated prisoner’s dilemma. J Econ Theory 39(1):83–96CrossRefGoogle Scholar
  36. Shiffrin RM (1976) Capacity limitations in information processing, attention, and memory. In: Estes WK (ed) Handbook of learning and cognitive processes, vol 4. Erlbaum, Hillsdale, pp 177–236Google Scholar
  37. Wilson TD, Nisbett RE (1978) The accuracy of verbal reports about the effects of stimuli on evaluations and behavior. Soc Psychol 41:118–131CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • M. Vittoria Levati
    • 1
    • 2
  • Matthias Uhl
    • 3
  • Ro’i Zultan
    • 4
  1. 1.Department of EconomicsUniversity of VeronaVeronaItaly
  2. 2.Max Planck Institute of EconomicsJenaGermany
  3. 3.TUM School of EducationTechnical University of MunichMunichGermany
  4. 4.Department of EconomicsBen-Gurion University of the NegevBeer-ShevaIsrael

Personalised recommendations