Linked bibliography for the SEP article "Common Knowledge" by Peter Vanderschraaf and Giacomo Sillari

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Annotations

Lewis (1969) is the classic pioneering study of common knowledge and its potential applications to conventions and game theory. As Lewis acknowledges, parts of his work are foreshadowed in Hume (1740) and Schelling (1960).

Aumann (1976) gives the first mathematically rigorous formulation of common knowledge using set theory. Schiffer (1972) uses the formal vocabulary of epistemic logic (Hintikka 1962) to state his definition of common knowledge. Schiffer's general approach is to augment a system of sentential logic with a set of knowledge operators corresponding to a set of agents, and then to define common knowledge as a hierarchy of propositions in the augmented system. Bacharach (1992), Bicchieri (1993) and Fagin, et al. (1995) adopt this approach, and develop logical theories of common knowledge which include soundness and completeness theorems. Fagin, et al. show that the syntactic and set-theoretic approaches to developing common knowledge are logically equivalent.

Aumann (1995) gives a recent defense of the classical view of backwards induction in games of imperfect information. For criticisms of the classical view, see Binmore (1987), Reny (1992), Bicchieri (1989) and especially Bicchieri (1993). Brandenburger (1992) surveys the known results connecting mutual and common knowledge to solution concepts in game theory. For more in-depth survey articles on common knowledge and its applications to game theory, see Binmore and Brandenburger (1989), Geanakoplos (1994) and Dekel and Gul (1996). For her alternate account of common knowledge along with an account of conventions which opposes Lewis' account, see Gilbert (1989).

Monderer and Samet (1989) remains one of the best resources for the study of common p-belief.

References

  • Alberucci, Luca and Jaeger, Gerhard, 2005, “About cut elimination for logics of common knowledge”, Annals of Pure and Applied Logic, 133(1–3): 73–99. (Scholar)
  • Aumann, Robert, 1974, “Subjectivity and Correlation in Randomized Strategies”, Journal of Mathematical Economics, 1: 67–96. (Scholar)
  • –––, 1976, “Agreeing to Disagree”, Annals of Statistics, 4: 1236–9. (Scholar)
  • –––, 1987, “Correlated Equilibrium as an Expression of Bayesian Rationality”, Econometrica, 55: 1–18. (Scholar)
  • –––, 1995, “Backward Induction and Common Knowledge of Rationality”, Games and Economic Behavior 8: 6–19. (Scholar)
  • Bacharach, Michael, 1989, “Mutual Knowledge and Human Reason”, mimeo. (Scholar)
  • Barwise, Jon, 1988, “Three Views of Common Knowledge”, in Proceedings of the Second Conference on Theoretical Aspects of Reasoning About Knowledge, M.Y. Vardi (ed.), San Francisco: Morgan Kaufman, pp. 365–379. (Scholar)
  • –––, 1989, The Situation in Logic, Stanford: Center for the Study of Language and Information. (Scholar)
  • Bernheim, B. Douglas, 1984, “Rationalizable Strategic Behavior”, Econometrica, 52: 1007–1028. (Scholar)
  • Bicchieri, Cristina, 1989, “Self Refuting Theories of Strategic Interaction: A Paradox of Common Knowledge”, Erkenntnis, 30: 69–85. (Scholar)
  • –––, 1993, Rationality and Coordination, Cambridge: Cambridge University Press. (Scholar)
  • –––, 2006, The Grammar of Society, Cambridge: Cambridge University Press. (Scholar)
  • Binmore, Ken, 1987, “Modelling Rational Players I”, Economics and Philosophy, 3: 179–241. (Scholar)
  • –––, 1992, Fun and Games, Lexington, MA: D. C. Heath. (Scholar)
  • –––, 2008, “Do conventions need to be common knowledge?”, Topoi, 27: 17–27. (Scholar)
  • Binmore, Ken and Brandenburger, Adam, 1988, “Common knowledge and Game theory” ST/ICERD Discussion Paper 88/167, London School of Economics. (Scholar)
  • Binmore, Ken and Samuelson, Larry, 2001, “Coordinated action in the electronic mail game” Games and Economic Behavior, 35(1): 6–30. (Scholar)
  • Bonanno, Giacomo and Battigalli, Pierpaolo, 1999, “Recent results on belief, knowledge and the epistemic foundations of game theory”, Research in Economics, 53(2): 149–225. (Scholar)
  • Bonnay, D. and Egré, Paul, 2009, “Inexact knowledge with introspection”, Journal of Philosophical Logic, 38: 179–227. (Scholar)
  • Brandenburger, Adam, 1992, “Knowledge and Equilibrium in Games”, Journal of Economic Perspectives, 6: 83–101. (Scholar)
  • Brandenburger, Adam, and Dekel, Eddie, 1987, “Common knowledge with Probability 1”, Journal of Mathematical Economics, 16: 237–245. (Scholar)
  • –––, 1988, “The Role of Common Knowledge Assumptions in Game Theory”, in The Economics of Missing Markets, Information and Games, Frank Hahn (ed.), Oxford: Clarendon Press, 46–61. (Scholar)
  • Carnap, Rudolf, 1947, Meaning and Necessity: A Study in Semantics and Modal Logic, Chicago, University of Chicago Press. (Scholar)
  • Chwe, Michael, 1999, “Structure and Strategy in Collective Action”, American Journal of Sociology 105: 128–56. (Scholar)
  • –––, 2000, “Communcation and Coordination in Social Networks”, Review of Economic Studies, 67: 1–16. (Scholar)
  • –––, 2001, Rational Ritual, Princeton, NJ: Princeton University Press (Scholar)
  • Cubitt, Robin and Sugden, Robert, 2003, “Common Knowledge, Salience and Convention: A Reconstruction of David Lewis' Game Theory”, Economics and Philosophy, 19: 175–210. (Scholar)
  • Dekel, Eddie and Gul, Faruk, 1996, “Rationality and Knowledge in Game Theory”, working paper, Northwestern and Princeton Universities. (Scholar)
  • Dekel, Eddie, Lipman, Bart and Rustichini, Aldo, 1998, “Standard state-space models preclude unawareness,” Econometrica, 66: 159–173. (Scholar)
  • Devetag, Giovanna, Hosni, Hykel and Sillari, Giacomo, 2013, “Play 7: mutual versus common knowledge of advice in a weak-link game,” Synthese, 190(8): 1351-1381 (Scholar)
  • Fagin, Ronald and Halpern, Joseph Y., 1988, “Awareness and Limited Reasoning,” Artificial Intelligence, 34: 39–76. (Scholar)
  • Fagin, Ronald, Halpern, Joseph Y., Moses, Yoram and Vardi, Moshe Y., 1995, Reasoning About Knowledge, Cambridge, MA: MIT Press. (Scholar)
  • Friedell, Morris, 1967, “On the Structure of Shared Awareness,” Working papers of the Center for Research on Social Organizations, Ann Arbor: University of Michigan, paper 27. (Scholar)
  • –––, 1969, “On the Structure of Shared Awareness,” Behavioral Science, 14(1): 28–39. (Scholar)
  • Geanakoplos, John, 1989, “Games theory without partitions, and applications to speculation and consensus,” Cowles Foundation Discussion Paper No. 914. (Scholar)
  • –––, 1994, “Common Knowledge”, in Handbook of Game Theory (Volume 2), Robert Aumann and Sergiu Hart (eds.), Amsterdam: Elsevier Science B.V., 1438–1496. (Scholar)
  • Gilbert, Margaret, 1989, On Social Facts, Princeton: Princeton University Press. (Scholar)
  • Halpern, Jospeh, 2001, “Alternative Semantics for Unawareness”, Games and Economic Behavior, 37(2): 321–339 (Scholar)
  • Harman, Gilbert, 1977, “Review of Linguistic Behavior by Jonathan Bennett”, Language, 53: 417–424. (Scholar)
  • Harsanyi, J., 1967, “Games with incomplete information played by ”Bayesian“ players, I: The basic model”, Management Science, 14: 159–82. (Scholar)
  • –––, 1968a, “Games with incomplete information played by ”Bayesian“ players, II: Bayesian equilibrium points”, Management Science, 14: 320–324. (Scholar)
  • –––, 1968b, “Games with incomplete information played by ”Bayesian“ players, III: The basic probability distribution of the game”, Management Science, 14: 486–502. (Scholar)
  • Heifetz, Aviad, 1999, “Iterative and Fixed Point Common Belief”, Journal of Philosophical Logic, 28(1): 61–79. (Scholar)
  • Heifetz, Aviad, Meier, Martin and Schipper, Burkhard, 2006, “Interactive unawareness”, Journal of Economic Theory, 130: 78–94. (Scholar)
  • Hintikka, Jaakko, 1962, Knowledge and Belief, Ithaca, New York: Cornell University Press. (Scholar)
  • Hume, David, 1740 [1888 1976], A Treatise of Human Nature, L. A. Selby-Bigge (ed.), rev. 2nd. edition P. H. Nidditch (ed.), Oxford: Clarendon Press. (Scholar)
  • Lewis, C. I., 1943, “The Modes of Meaning”, Philosophy and Phenomenological Research, 4: 236–250. (Scholar)
  • Lewis, David, 1969, Convention: A Philosophical Study, Cambridge, MA: Harvard University Press. (Scholar)
  • –––, 1978, “Truth in Fiction”, American Philosophical Quarterly, 15: 37–46. (Scholar)
  • Littlewood, J. E., 1953, A Mathematical Miscellany, London: Methuen; reprinted as Littlewood's Miscellany, B. Bollobas (ed.), Cambridge: Cambridge University Press, 1986. (Scholar)
  • McKelvey, Richard and Page, Talbot, 1986, “Common knowledge, consensus and aggregate information”, Econometrica, 54: 109–127. (Scholar)
  • Meyer, J.-J.Ch. and van der Hoek, Wiebe, 1995, Epistemic Logic for Computer Science and Artificial Intelligence (Cambridge Tracts in Theoretical Computer Science 41), Cambridge: Cambridge University Press. (Scholar)
  • Milgrom, Paul, 1981, “An axiomatic characterization of common knowledge”, Econometrica, 49: 219–222. (Scholar)
  • Monderer, Dov and Samet, Dov, 1989, “Approximating Common Knowledge with Common Beliefs”, Games and Economic Behavior, 1: 170–190. (Scholar)
  • Nash, John, 1950, “Equilibrium points in n-person games”. Proceedings of the National Academy of Sciences of the United States, 36: 48–49. (Scholar)
  • –––, 1951, “Non-Cooperative Games”. Annals of Mathematics, 54: 286–295. (Scholar)
  • Nozick, Robert, 1963, The Normative Theory of Individual Choice, Ph.D. dissertation, Princeton University (Scholar)
  • Pearce, David, 1984, “Rationalizable Strategic Behavior and the Problem of Perfection”. Econometrica, 52: 1029–1050. (Scholar)
  • Reny, Philip, 1987, “Rationality, Common Knowledge, and the Theory of Games”, working paper, Department of Economics, University of Western Ontario. (Scholar)
  • –––, 1992, “Rationality in Extensive Form Games”, Journal of Economic Perspectives, 6: 103–118. (Scholar)
  • Rubinstein, Ariel, 1987, “A Game with ”Almost Common Knowledge“: An Example”, in Theoretical Economics, D. P. 87/165. London School of Economics. (Scholar)
  • Samet, Dov, 1990, “Ignoring Ignorance and Agreeing to Disagree”, Journal of Economic Theory, 52: 190–207. (Scholar)
  • Schelling, Thomas, 1960, The Strategy of Conflict, Cambridge, MA: Harvard University Press. (Scholar)
  • Schiffer, Stephen, 1972, Meaning, Oxford: Oxford University Press. (Scholar)
  • Sillari, Giacomo, 2005, “A Logical Framework for Convention”, Synthese, 147(2): 379–400. (Scholar)
  • –––, 2008, “Common Knowledge and Convention”, Topoi, 27(1): 29–39. (Scholar)
  • Skyrms, Brian, 1984, Pragmatics and Empiricism, New Haven: Yale University Press. (Scholar)
  • Stinchcombe, Max, 1988, “Approximate Common Knowledge”, mimeo, San Diego: University of California. (Scholar)
  • Sugden, Robert, 1986, The Economics of Rights, Cooperation and Welfare, New York: Basil Blackwell. (Scholar)
  • Vanderschraaf, Peter, 1995, “Endogenous Correlated Equilibria in Noncooperative Games”, Theory and Decision, 38: 61–84. (Scholar)
  • Vanderschraaf, Peter, 1998, “Knowledge, Equilibrium and Convention”, Erkenntnis, 49: 337–369. (Scholar)
  • –––, 2001. A Study in Inductive Deliberation, New York: Routledge. (Scholar)
  • von Neumann, John and Morgenstern, Oskar, 1944, Theory of Games and Economic Behavior, Princeton: Princeton University Press. (Scholar)

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