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Common Knowledge and Davis's Argument from Symmetry in the Prisoner's Dilemma

Published online by Cambridge University Press:  13 April 2010

Richard Reiner
Affiliation:
University of Toronto

Extract

Lawrence H. Davis (1977, 1985) has formulated and defended a version of the argument from symmetry for the non-iterated Prisoner's Dilemma that attempts to show that under certain conditions the rationally prescribed course of action in this game is co-operation. The argument runs as follows below. (I have prefixed a ‘D’ to each of Davis's numbers here, and in subsequent references, in order to avoid confusion as I refer to his points.)

Type
Articles
Copyright
Copyright © Canadian Philosophical Association 1995

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References

Aumann, Robert J. 1976Agreeing to Disagree.” Annals of Statistics, 4,6 (1976): 1236–39.CrossRefGoogle Scholar
Barwise, Jon 1988a The Situation in Logic. Stanford, CT: Center for the Study of Language and Information.Google Scholar
Barwise, Jon 1988b “Three Views of Common Knowledge.” In Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge. Edited by Vardi, Moshe Y.. Los Altos, CA: Morgan Kaufman.Google Scholar
Barwise, Jon 1988c “On the Model Theory of Common Knowledge.” In Jon Barwise, The Situation in Logic. Stanford, CT: Center for the Study of Language and Information.Google Scholar
Barwise, Jon 1988d “Situations, Sets, and the Axiom of Foundation.” In Jon Barwise, The Situation in Logic. Stanford, CT: Center for the Study of Language and Information.Google Scholar
Basu, Kaushik 1987Modeling Finitely-Repeated Games with Uncertain Termination.” Economics Letters, 23: 147–51.Google Scholar
Bicchieri, Cristina 1988 “Common Knowledge and Backward Induction: A Solution to the Paradox.” In Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge. Edited by Vardi, Moshe Y.. Los Altos, CA: Morgan Kaufman.Google Scholar
Campbell, Richmond 1985 “Background for the Uninitiated.” In Paradoxes of Rationality and Cooperation: Prisoner's Dilemma and Newcomb's Problem. Edited by Campbell, Richmond and Snowden, Lanning. Vancouver, BC: University of British Columbia Press.Google Scholar
Richmond, Campbell, and Sowden, Lanning, eds. 1985 Paradoxes of Rationality and Cooperation: Prisoner's Dilemma and Newcomb's Problem. Vancouver, BC: University of British Columbia Press.Google Scholar
Clark, Herbert H., and Marshall, Catherine R. 1981 “Definite Reference and Mutual Knowledge.” In Elements of Discourse Understanding. Cambridge: Cambridge University Press.Google Scholar
Daughety, Andrew F., and Forsythe, Robert 1988 “Complete Information Outcomes without Common Knowledge.” In Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge. Edited by Vardi, Moshe Y.. Los Altos, CA: Morgan Kaufman.Google Scholar
Davis, Lawrence H. 1985a “Prisoners, Paradox, and Rationality.” 1977. Rpt. In Paradoxes of Rationality and Cooperation: Prisoner's Dilemma and Newcomb's Problem. Edited by Campbell, Richmond and Snowden, Lanning. Vancouver, BC: University of British Columbia Press. Originally appeared i n the American Philosophical Quarterly, 14,4 (October): 319–27.Google Scholar
Davis, Lawrence H. 1985b “Is the Symmetry Argument Valid?” In Paradoxes of Rationality and Cooperation: Prisoner's Dilemma and Newcomb's Problem. Edited by Campbell, Richmond and Snowden, Lanning. Vancouver, BC: University of British Columbia Press.Google Scholar
Dretske, Fred I. 1981 Knowledge and the Flow of Information. Cambridge, MA: MIT Press.Google Scholar
Dwork, Cynthia, and Moses, Yoram 1986 “Knowledge and Common Knowledge in a Byzantine Environment I: Crash Failures (Extended Abstract).” In Proceedings of the 1986 Conference on Theoretical Aspects of Reasoning about Knowledge. Edited by Halpern, Joseph Y.. Los Altos, CA: Morgan Kaufman.Google Scholar
Gauthier, David 1985 Morals by Agreement. Oxford: Oxford University Press.Google Scholar
Gibbard, Allan, and Harper, William L. 1978 “Counterfactuals and Two Kinds of Expected Utility.” In Paradoxes of Rationality and Cooperation: Prisoner's Dilemma and Newcomb's Problem. Edited by Campbell, Richmond and Snowden, Lanning. Vancouver, BC: University of British Columbia Press.Google Scholar
Gilboa, Itzhak 1988 “Information-Independent Games: Common Sense without Common Knowledge? (Extended Abstract).” In Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge Edited by Vardi, Moshe Y.. Los Altos, CA: Morgan Kaufman.Google Scholar
Halpern, Joseph Y., ed. 1986 Proceedings of the 1986 Conference on Theoretical Aspects of Reasoning about Knowledge. Los Altos, CA: Morgan Kaufman.Google Scholar
Harman, Gilbert 1977 Review of Jonathan Bennett's Linguistic Behaviour. Language, 53,2: 417–24.CrossRefGoogle Scholar
Hintikka, Jaako 1961 Knowledge and Belief: An Introduction to the Logic of the Two Notions. Ithaca, NY: Cornell University Press.Google Scholar
Horgan, Terence 1985 “Counterfactuals and Newcomb's Problem.” 1981. Rpt. In Paradoxes of Rationality and Cooperation: Prisoner's Dilemma and Newcomb's Problem. Edited by Campbell, Richmond and Snowden, Lanning. Vancouver, BC: University of British Columbia Press. Originally appeared in the Journal of Philosophy, 78,6 (June 1981) 331–56.Google Scholar
Joshi, Aravind K., Webber, Bonnie L. and Sag, Ivan A., eds. 1981 Elements of Discourse Understanding. Cambridge: Cambridge University Press.Google Scholar
Lewis, David K. 1969 Convention: A Philosophical Study. Cambridge, MA: Harvard University Press.Google Scholar
McCarthy, John, Sato, M., Igarashi, S. and Hayashi, T. 1977 “On the Model Theory of Knowledge.” Unpublished paper. Was to appear in Proceedings of IJCAI-77 (Fourth International Joint Conference on Artificial Intelligence). Cambridge, MA: MIT Press.Google Scholar
Milgrom, Paul 1981An Axiomatic Characterization of Common Knowledge.” Econo-metrica, 49,1 (January) 219–22.Google Scholar
Schiffer, Stephen S. 1972 Meaning. Oxford: Clarendon Press.Google Scholar
Smith, N. V, ed. 1982 Mutual Knowledge. London: Academic Press.Google Scholar
Tan, Tommy C, and Werlang, Sergio R. D. C. 1986 “Summary of ‘On Aumann's Notion of Common Knowledge—An Alternative Approach’.” In Proceedings of the 1986 Conference on Theoretical Aspects of Reasoning about Knowledge Edited by Halpern, Joseph Y.. Los Altos, CA: Morgan Kaufman.Google Scholar
Tan, Tommy C, and Werlang, Sergio R. D. C. 1988 “A Guide to Knowledge and Games.” In Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge. Edited by Vardi, Moshe Y.. Los Altos, CA: Morgan Kaufman.Google Scholar
Vardi, Moshe Y., ed. 1988 Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge. Los Altos, CA: Morgan Kaufman.Google Scholar