Skip to main content
SpringerLink
Log in

You better play 7: mutual versus common knowledge of advice in a weak-link experiment

  • Published:
Synthese Aims and scope Submit manuscript

Abstract

This paper presents the results of an experiment on mutual versus common knowledge of advice in a two-player weak-link game with random matching. Our experimental subjects play in pairs for thirteen rounds. After a brief learning phase common to all treatments, we vary the knowledge levels associated with external advice given in the form of a suggestion to pick the strategy supporting the payoff-dominant equilibrium. Our results are somewhat surprising and can be summarized as follows: in all our treatments both the choice of the efficiency-inducing action and the percentage of efficient equilibrium play are higher with respect to the control treatment, revealing that even a condition as weak as mutual knowledge of level 1 is sufficient to significantly increase the salience of the efficient equilibrium with respect to the absence of advice. Furthermore, and contrary to our hypothesis, mutual knowledge of level 2 induces, under suitable conditions, successful coordination more frequently than common knowledge.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Allo P. (2011) The logic of being informed revisited and revised. Philosophical Studies 153(3): 417–434

    Article  Google Scholar 

  • Aumann R. J. (1976) Agreeing to disagree. Annals of Statistics 4: 1236–1239

    Article  Google Scholar 

  • Aumann R. J. (1987) Correlated equilibrium as an expression of Bayesian rationality. The Econometric Society 55(1): 1–18

    Article  Google Scholar 

  • Aumann R. J. (1999) Interactive epistemology I: Knowledge. International Journal of Game Theory 28: 263–300

    Article  Google Scholar 

  • Aumann R. J., Brandenburger A. (1995) Epistemic conditions for Nash equilibrium. Econometrica 63(5): 1161–1180

    Article  Google Scholar 

  • Aumann R. J., Brandenburger A. (2008) Epistemic game theory: An overview. In: Durlauf S., Blume L. (eds) The new Palgrave dictionary of economics. Palgrave Macmillan, New York

    Google Scholar 

  • Bacharach M., Bernasconi M. (1997) The variable frame theory of focal points: An experimental study. Games and Economic Behavior 19(1): 1–45

    Article  Google Scholar 

  • Bangun L., Chaudhuri A., Prak P., Zhou C. (2006) Common and almost common knowledge of credible assignments in a coordination game. Economics Bulletin 3: 1–10

    Google Scholar 

  • Bicchieri C. (2006) The grammar of society. Cambridge University Press, Cambridge, MA

    Google Scholar 

  • Bicchieri C., Chavez A. (2010) Behaving as expected: Public information and fairness norms. Journal of Behavioral Decision Making 23: 161–178

    Article  Google Scholar 

  • Bicchieri C., Chavez A., Lev-On A. (2010) The medium or the message? Communication relevance and richness in trust games. Synthese 176: 125–147

    Article  Google Scholar 

  • Bicchieri C., Lev-On A. (2007) Computer-mediated communication and cooperation in social dilemmas. Philosophy, Politics and Economics 6: 139–168

    Article  Google Scholar 

  • Bicchieri C., Xiao E. (2009) Do the right thing: But only if others do so. Journal of Behavioral Decision Making 22: 191–208

    Article  Google Scholar 

  • Binmore K. (2008) Do conventions need to be common knowledge?. Topoi 27: 17–27

    Article  Google Scholar 

  • Blackburn P., de Rijke M., Venema Y. (2001) Modal logic. Cambridge University Press, Cambridge, MA

    Google Scholar 

  • Blackburn P., Van Benthem J., Wolter F. (2007) Handbook of modal logic. Elsevier, Amsterdam

    Google Scholar 

  • Camerer C. (2003) Behavioral game theory. Experiments in strategic interaction. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Camerer C., Knez M. (1996) Coordination, organizational boundaries and fads in business practice. Industrial and Corporate Change 5: 89–112

    Article  Google Scholar 

  • Camerer, C., & Knez, M. (1997). Coordination in organizations: A game-theoretic perspective. In Z. Shapira (Ed.), Organizational decision making (pp. 158–188). Cambridge, MA: Cambridge Series on Judgment and Decision Making.

  • Chaudhuri A., Paichayontvijit T. (2010) Recommended play and performance bonuses in the minimum effort coordination game. Experimental Economics 13: 346–363

    Article  Google Scholar 

  • Chaudhuri A., Sopher B., Schotter A. (2009) Talking ourselves to efficiency: Coordination in inter-generational minimum effort games with private, almost common and common knowledge of advice. Economic Journal 119(534): 91–122

    Article  Google Scholar 

  • Cooper R., De Jong D., Forsythe R., Ross T. (1990) Selection criteria in coordination games: Some experimental results. American Economic Review 80: 218–233

    Google Scholar 

  • Cooper R., De Jong D., Forsythe R., Ross T. (1992) Communication in coordination games. Quarterly Journal of Economics 107: 739–771

    Article  Google Scholar 

  • Cubitt R. P., Sugden R. (2003) Common knowledge, salience and convention: A reconstruction of David Lewis’ game theory. Economics and Philosophy 19: 175–210

    Article  Google Scholar 

  • D’Agostino M. (2010) Tractable depth-bounded logics and the problem of logical omniscience. In: Hosni H., Montagna F. (eds) Probability, uncertainty and rationality. Edizioni della Normale, Pisa, pp 245–275

    Google Scholar 

  • Devetag G., Ortmann A. (2007) When and why? A critical survey on coordination failure in the laboratory. Experimental Economics 10: 331–344

    Article  Google Scholar 

  • Fagin R., Halpern J. Y., Yoram M., Vardi M. (1996) Reasoning about knowledge. MIT Press, Cambridge, MA

    Google Scholar 

  • Friedman D., Sunder S. (1994) Experimental methods: A primer for economists. Cambridge University Press, Cambridge, MA

    Book  Google Scholar 

  • Halpern, J. Y., & Pcella, R. (2007). Dealing with logical omniscience. In Proceedings of the 11th conference on theoretical aspects of rationality and knowledge. ACM.

  • Halpern J. Y., Rêgo L. (2008) Interactive unawareness revisited. Games and Economic Behavior 62(1): 232–262

    Article  Google Scholar 

  • Harsanyi J., Selten R. (1988) A general theory of equilibrium selection in games. The MIT Press, Cambridge, MA

    Google Scholar 

  • Hendricks V. F. (2005) Mainstream and formal epistemology. Cambridge University Press, Cambridge, MA

    Book  Google Scholar 

  • Hintikka J. (1962) Knowledge and belief. Cornell University Press, Ithaca, NY

    Google Scholar 

  • Hosni H., Paris J. (2005) Rationality as conformity. Synthese 144(2): 249–285

    Article  Google Scholar 

  • Knez M., Simester D. (2001) Firm-wide incentives and mutual monitoring at Continental Airlines. Journal of Labor Economics 19: 743–772

    Article  Google Scholar 

  • Lewis D. K. (1969) Convention: A philosophical study. Harvard University Press, Cambridge, MA

    Google Scholar 

  • Metha J., Starmer C., Sugden R. (1994) The nature of salience: An experimental investigation of pure coordination games. American Economic Review 84: 658–673

    Google Scholar 

  • Meyer J.-J.Ch., van~der Hoek W. (1995) Epistemic logic for AI and computer science. Cambridge University Press, Cambridge, MA

    Book  Google Scholar 

  • Parikh R. (2002) Social software. Synthese 2(132): 187–211

    Article  Google Scholar 

  • Parikh, R. (2005). Logical omniscience and common knowledge: WHAT do we know and what do WE. In Theoretical aspects of rationality and knowledge (pp. 62–77).

  • Rescorla, M. (2011). Convention. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Spring 2011 edition). Accessed January 2012, from http://plato.stanford.edu/archives/spr2011/entries/convention/ .

  • Rubinstein A. (1989) The electronic mail game: Strategic behavior under “almost common knowledge”. American Economic Review 79: 385–391

    Google Scholar 

  • Schelling T. (1980) The strategy of conflict. Harvard University Press, Cambridge, MA

    Google Scholar 

  • Schipper, B. (2012). In B. Schipper (Ed.), Unawareness bibliography. Accessed January 2012, from http://www.econ.ucdavis.edu/faculty/schipper/unaw.htm .

  • Sillari G. (2008) Common knowledge and convention. Topoi 27: 29–39

    Article  Google Scholar 

  • Skyrms B. (1996) The evolution of the social contract. Cambridge University Press, Cambridge, MA

    Book  Google Scholar 

  • Sugden, R. (1986). The economics of right, co-operation and welfare (2nd ed., 2004). New York: Palgrave Macmillan.

  • Ullman-Margalit E. (1977) The emergence of norms. Clarendon Press, Oxford

    Google Scholar 

  • van Benthem J. (2008) Logic and reasoning: Do the facts matter?. Studia Logica 88: 67–84

    Article  Google Scholar 

  • van Ditmarsch H., van Der Hoek W., Kooi B. (2007) Dynamic epistemic logic. Springer, New York

    Google Scholar 

  • Van Huyck J. B., Beil R. O., Gillette A., Battalio R. C. (1990) Tacit coordination games, strategic uncertainty, and coordination failure. The American Economic Review 80: 234–248

    Google Scholar 

  • Van Huyck J. B., Gillette A., Battalio R. C. (1992) Credible assignments in coordination games. Games and Economic Behavior 4: 606–626

    Article  Google Scholar 

  • Vanderschraaf P. (1995) Convention as correlated equilibrium. Erkenntnis 42: 65–87

    Article  Google Scholar 

  • Vanderschraaf, P., & Sillari, G. (2007). Common knowledge. In E. N. Zalta (Ed.), Stanford encyclopedia of philosophy (Spring 2009 edition), Accessed January 2012, from http://plato.stanford.edu/entries/common-knowledge/ .

  • Verbrugge R. (2009) Logic and social cognition: The facts matter, and so do computational models. Journal of Philosophical Logic 38: 649–680

    Article  Google Scholar 

  • Young P. (1998) Individual strategy and social structure: An evolutionary theory of institutions. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Zizzo D. (2010) Experimenter demand effect in economic experiments. Experimental Economics 13: 75–98

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Perugia, Via Pascoli 20, 06123, Perugia, Italy

    Giovanna Devetag

  2. Scuola Normale Superiore, Piazza dei Cavalieri 7, 56100, Pisa, Italy

    Hykel Hosni & Giacomo Sillari

Authors
  1. Giovanna Devetag
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hykel Hosni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Giacomo Sillari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giacomo Sillari.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Devetag, G., Hosni, H. & Sillari, G. You better play 7: mutual versus common knowledge of advice in a weak-link experiment. Synthese 190, 1351–1381 (2013). https://doi.org/10.1007/s11229-012-0177-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11229-012-0177-9

Keywords

Search

Navigation