Advertisement

International Journal of Game Theory

, Volume 42, Issue 4, pp 789–800 | Cite as

Timing of messages and the Aumann conjecture: a multiple-selves approach

  • Ro’i Zultan
Article

Abstract

The Aumann (In: Gabszewicz JJ, Richard JF, Wolsey L (eds) Economic decision making: games, econometrics and optimisation, 1990) conjecture states that cheap-talk messages do not necessarily help to coordinate on efficient Nash equilibria. In an experimental test of Aumann’s conjecture, Charness (Games Econ Behav 33(2):177–194, 2000) found that cheap-talk messages facilitate coordination when they precede the action, but not when they follow the action. Standard game-theoretical modeling abstracts from this timing effect, and therefore cannot account for it. To allow for a formal analysis of the timing effect, I study the sequential equilibria of the signaling game in which the sender is modeled as comprising two selves: an acting self and a signaling self. I interpret Aumann’s argument in this context to imply that all of the equilibria in this game are ‘babbling’ equilibria, in which the message conveys no information and does not affect the behavior of the receiver. Using this framework, I show that a fully communicative equilibrium exists—only if the message precedes the action but not when the message follows the action. In the latter case, no information is transmitted in any equilibrium. This result provides a game-theoretical explanation for the puzzling experimental results obtained by Charness (2000). I discuss other explanations for this timing-of-message effect and their relationship to the current analysis.

Keywords

Pre-play communication Nash equilibrium Coordination games Multiple selves 

JEL Classification

A13 C72 C91 D82 D84 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aumann RJ (1990) Nash-equilibria are not self-enforcing. In: Gabszewicz JJ, Richard JF, Wolsey L (eds) Economic decision making: games, econometrics and optimisation. North-Holland, Amsterdam, pp 201–206Google Scholar
  2. Aumann RJ, Hart S, Perry M (1997) The absent-minded driver. Games Econ Behav 20(1): 102–116CrossRefGoogle Scholar
  3. Battigalli P, Dufwenberg M (2007) Guilt in games. Am Econ Rev 97(2): 170–176CrossRefGoogle Scholar
  4. Blume A, Ortmann A (2007) The effects of costless pre-play communication: experimental evidence from games with pareto-ranked equilibria. J Econ Theory 132(1): 274–290CrossRefGoogle Scholar
  5. Charness G (2000) Self-serving cheap talk: a test of Aumann’s conjecture. Games Econ Behav 33(2): 177–194CrossRefGoogle Scholar
  6. Charness G, Dufwenberg M (2006) Promises and partnership. Econometrica 74(6): 1579–1601CrossRefGoogle Scholar
  7. Charness G, Dufwenberg M (2011) Participation. Am Econ Rev 101(4): 1211–1237CrossRefGoogle Scholar
  8. Clark K, Kay S, Sefton M (2001) When are Nash equilibria self-enforcing? An experimental analysis. Int J Game Theory 29(4): 495–515CrossRefGoogle Scholar
  9. Cooper R, DeJong DV, Forsythe R, Ross TW (1992) Communication in coordination games. Q J Econ 107(2): 739–771CrossRefGoogle Scholar
  10. Crawford VP (1998) A survey of experiments on communication via cheap talk. J Econ Theory 78(2): 286–298CrossRefGoogle Scholar
  11. Crawford VP, Sobel J (1982) Strategic information transmission. Econom J Econom Soc 50(6): 1431–1451Google Scholar
  12. Ellingsen T, Johannesson M (2004) Promises, threats and fairness. Econ J 114(495): 397–420CrossRefGoogle Scholar
  13. Farrell J (1988) Communication, coordination and Nash equilibrium. Econ Lett 27(3): 209–214CrossRefGoogle Scholar
  14. Farrell J (1993) Meaning and credibility in cheap-talk games. Games Econ Behav 5(4): 514–531CrossRefGoogle Scholar
  15. Farrell J, Rabin M (1996) Cheap talk. J Econ Perspect 10(3): 103–118CrossRefGoogle Scholar
  16. Fudenberg D, Levine DK (2006) A dual-self model of impulse control. Am Econ Rev 96(5): 1449–1476CrossRefGoogle Scholar
  17. Gilboa I (1997) A comment on the absent-minded driver paradox. Games Econ Behav 20(1): 25–30CrossRefGoogle Scholar
  18. Gneezy U (2005) Deception: the role of consequences. Am Econ Rev 95(1): 384–394CrossRefGoogle Scholar
  19. Halpern JY (1997) On ambiguities in the interpretation of game trees. Games Econ Behav 20(1): 66–96CrossRefGoogle Scholar
  20. Harsanyi JC (1995) A new theory of equilibrium selection for games with incomplete information. Games Econ Behav 10(2): 318–332CrossRefGoogle Scholar
  21. Harsanyi JC, Selten R (1988) A general theory of equilibrium selection in games. MIT Press, CambridgeGoogle Scholar
  22. Hurkens S, Kartik N (2009) Would I lie to you? On social preferences and lying aversion. Exp Econ 12(2): 180–192CrossRefGoogle Scholar
  23. Luce RD (1990) Rational versus plausible accounting equivalences in preference judgments. Psychol Sci 1(4): 225–234CrossRefGoogle Scholar
  24. Moldoveanu M, Stevenson H (2001) The self as a problem: the intra-personal coordination of conflicting desires. J Socio-Econ 30(4): 295–330CrossRefGoogle Scholar
  25. Palfrey TR, Rosenthal H (1991) Testing for effects of cheap talk in a public goods game with private information. Games Econ Behav 3(2): 183–220CrossRefGoogle Scholar
  26. Piccione M, Rubinstein A (1997) On the interpretation of decision problems with imperfect recall. Games Econ Behav 20(1): 3–24CrossRefGoogle Scholar
  27. Rapoport A (1997) Order of play in strategically equivalent games in extensive form. Int J Game Theory 26: 113–126CrossRefGoogle Scholar
  28. Schelling TC (1984) Self-command in practice, in policy, and in a theory of rational choice. Am Econ Rev 74(2): 1–11Google Scholar
  29. Strotz RH (1955) Myopia and inconsistency in dynamic utility maximization. Rev Econ Stud 23(3): 165–180CrossRefGoogle Scholar
  30. Thaler RH, Shefrin HM (1981) An economic theory of self-control. J Political Econ 89(2): 392–406CrossRefGoogle Scholar
  31. Valley K, Thompson L, Gibbons R, Bazerman MH (2002) How communication improves efficiency in bargaining games. Games Econ Behav 38(1): 127–155CrossRefGoogle Scholar
  32. Vanberg C (2008) Why do people keep their promises? An experimental test of two explanations. Econometrica 76(6): 1467–1480CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of EconomicsBen-Gurion University of the NegevBeer ShevaIsrael

Personalised recommendations