Topoi

, 27:17

Do Conventions Need to Be Common Knowledge?

Article

Abstract

Do conventions need to be common knowledge in order to work? David Lewis builds this requirement into his definition of a convention. This paper explores the extent to which his approach finds support in the game theory literature. The knowledge formalism developed by Robert Aumann and others militates against Lewis’s approach, because it shows that it is almost impossible for something to become common knowledge in a large society. On the other hand, Ariel Rubinstein’s Email Game suggests that coordinated action is no less hard for rational players without a common knowledge requirement. But an unnecessary simplifying assumption in the Email Game turns out to be doing all the work, and the current paper concludes that common knowledge is better excluded from a definition of the conventions that we use to regulate our daily lives.

Keywords

Conventions Common knowledge Game theory 

References

  1. Aumann R (1976) Agreeing to disagree. Ann Stat 4:1236–1239CrossRefGoogle Scholar
  2. Binmore K (1987) Modeling rational players I. Econ Phil 3:9–55CrossRefGoogle Scholar
  3. Binmore K (1994) Playing fair: game theory and the social contract I. MIT Press, Cambridge, MAGoogle Scholar
  4. Binmore K (2005) Natural justice. Oxford University Press, New YorkGoogle Scholar
  5. Binmore K (2007) Does game theory work? The bargaining challenge. MIT Press, Cambridge MAGoogle Scholar
  6. Binmore K (2007) Playing for real. Oxford University Press, New YorkGoogle Scholar
  7. Binmore K, Samuelson L (2001) Coordinated action in the electronic mail game. Games Econ Behav 35:6–30CrossRefGoogle Scholar
  8. Binmore K, Swierzbinski J, Hsu S, Proulx C (1993) Focal points and bargaining. Int J Game Theory 22:381–409CrossRefGoogle Scholar
  9. Cubitt R, Sugden R (2005) Common reasoning in game theory: a resolution of the paradoxes of ‘common knowledge of rationality’. Centre for Decision Research and Experimental Economics 17, School of Economics, University of NottinghamGoogle Scholar
  10. Halpern JY (1987) Using reasoning about knowledge to analyse distributed systems. Annu Rev Comp Sci 2:37–68CrossRefGoogle Scholar
  11. Harsanyi J (1977) Rational behavior and bargaining equilibrium in games and social situations. Cambridge University Press, CambridgeGoogle Scholar
  12. Hume, D (1978) A treatise of human nature, 2nd edn. Clarendon Press, Oxford (edited by Selby-Bigge LA, revised by Nidditch P, first published 1739)Google Scholar
  13. Kalai E, Smorodinsky M (1975) Other solutions to Nash’s bargaining problem. Econometrica 45:1623–1630CrossRefGoogle Scholar
  14. Lewis D (1969) Convention: a philosophical study. Harvard University Press, Cambridge, MAGoogle Scholar
  15. Maynard Smith J (1982) Evolution and the theory of games. Cambridge University Press, CambridgeGoogle Scholar
  16. Monderer D, Samet D (1989) Approximating common knowledge with common beliefs. Games Econ Behav 1:170–190CrossRefGoogle Scholar
  17. Myerson R (1991) Game theory: analysis of conflict. Harvard University Press, Cambridge, MAGoogle Scholar
  18. Nash J (1950) The bargaining problem. Econometrica 18:155–162CrossRefGoogle Scholar
  19. Nash J (1951) Non-cooperative games. Ann Math 54:286–295CrossRefGoogle Scholar
  20. Rawls J (1972) A theory of justice. Oxford University Press, OxfordGoogle Scholar
  21. Rousseau J-J (1913) The inequality of man. In: Cole G (ed) Rousseau’s social contract and discourses. Dent, LondonGoogle Scholar
  22. Rubinstein A (1989) The electronic mail game: strategic behavior under almost common knowledge. Am Econ Rev 70:385–391Google Scholar
  23. Schelling T (1960) The strategy of conflict. Harvard University Press, Cambridge MAGoogle Scholar
  24. Skyrms B (1996) Evolution of the social contract. Cambridge University Press, CambridgeGoogle Scholar
  25. Skyrms B (2003) The stag hunt and the evolution of the social structure. Cambridge University Press, CambridgeGoogle Scholar
  26. Turnbull C (1972) The mountain people. Touchstone, New YorkGoogle Scholar
  27. Von Neumann J, Morgenstern O (1944) The theory of games and economic behavior. Princeton University Press, PrincetonGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Philosophy DepartmentBristol UniversityBristolUK

Personalised recommendations