Hostname: page-component-68945f75b7-jkr4m Total loading time: 0 Render date: 2024-09-04T09:14:46.107Z Has data issue: false hasContentIssue false
  • English
  • Français

Newcomb's Problem and Repeated Prisoners’ Dilemmas

Published online by Cambridge University Press:  01 January 2022

Christoph Schmidt-Petri
Get access Rights & Permissions [Opens in a new window]

Abstract

I present a game-theoretic way to understand the situation describing Newcomb's Problem (NP) which helps to explain the intuition of both one-boxers and two-boxers. David Lewis has shown that the NP may be modelled as a Prisoner's Dilemma game (PD) in which ‘cooperating’ corresponds to ‘taking one box’. Adopting relevant results from game theory, this means that one should take just one box if the NP is repeated an indefinite number of times, but both boxes if it is a one-shot game. Causal decision theorists thus give the right answer for the one-shot situation, whereas the one-boxers’ solution applies to the indefinitely iterated case. Because Nozick's set-up of the NP is ambiguous between a one-shot and a repeated game, both of these solutions may appear plausible—depending on whether one conceives of the situation as one-off or repeated. If the players’ aim is to maximize their payoffs, the symmetric structure of the PD implies that the two players will behave alike both when the game is one-shot and when it is played repeatedly. Therefore neither the observed outcome of both players selecting the same strategy (in the PD) nor, correspondingly, the predictor's accurate prediction of this outcome (in the NP) is at all surprising. There is no need for a supernatural predictor to explain the NP phenomena.

Type
Decision Theory
Information
Philosophy of Science , Volume 72 , Issue 5: Proceedings of the 2004 Biennial Meeting of The Philosophy of Science Association. Part I: Contributed Papers , December 2005 , pp. 1160 - 1173
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

I am grateful for helpful comments and criticisms by Jason Alexander, Richard Arneson, Thomas Baldwin, Jossi Berkovitz, Richard Bradley, Luc Bovens, Juliana Cardinale, Nancy Cartwright, John Collins, Peter Dietsch, Adam Elga, Branden Fitelson, Till Grüne-Yanoff, Jonathan Halvorson, Jim Joyce, Isaac Levi, Ned McClennen, Paul Schweinzer, Dana Tulodziecki, Bruno Verbeek, Ioannis Votsis, and Jo Wolff. Special thanks to Ulrich K. Müller. I gratefully acknowledge financial support from the AHRB, the Aristotelian Society, the Department of Philosophy, Logic and Scientific Method of the London School of Economics, as well as the Philosophy, Probability and Modeling Group at Konstanz, which was supported by the Alexander von Humboldt Foundation, the Federal Ministry of Education and Research, and the Program for the Investment in the Future (ZIP) of the German Government through a Sofja Kovalevskaja Award to Luc Bovens.

References

Bar-Hillel, M., and Margalit, A. (1972), “Newcomb’s Paradox Revisited”, Newcomb’s Paradox Revisited 23:295–304.Google Scholar
Bicchieri, C., and Green, M. S. (1997), “Symmetry Arguments for Cooperation in the Prisoner’s Dilemma”, in G. Holmstrom-Hintikka and R. Tuomela (eds.), Contemporary Action Theory, vol. II, The Philosophy and Logic of Social Action. Dordrecht: Kluwer, 229–249.Google Scholar
Binmore, K. (1992), Fun and Games. Lexington, MA: Heath.Google Scholar
Binmore, K. (1994), Playing Fair: Game Theory and the Social Contract, Vol. I. Cambridge, MA: MIT Press.Google Scholar
Brams, S. (1975), “Newcomb’s Problem and Prisoners’ Dilemma”, Newcomb’s Problem and Prisoners’ Dilemma 19:596–612.Google Scholar
Cargile, J. (1975), “Newcomb’s Paradox”, Newcomb’s Paradox 26:234–239.Google Scholar
Davis, L. H. ([1977] 1985), “Prisoners, Paradox, and Rationality”, in Campbell, R. and Sowden, L. (eds.), Paradoxes of Rationality and Cooperation. Vancouver: University of British Columbia Press, 45–58. Originally published in American Philosophical Quarterly 14:319–327.Google Scholar
Davis, L. H. (1985), “Is the Symmetry Argument Valid?”, in Campbell, R. and Sowden, L. (eds.), Paradoxes of Rationality and Cooperation. Vancouver: University of British Columbia Press, 255–263.Google Scholar
Eells, E. (1982), Rational Decision and Causality. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Fudenberg, D., and Tirole, J. (1991), Game Theory. Cambridge, MA: MIT Press.Google Scholar
Gibbard, Allan, and Harper, W. (1978), “Counterfactuals and Two Kinds of Expected Utility”, in Hooker, C. A., Leach, J. J., and McClennen, E. F. (eds.), Foundations and Applications of Decision Theory, vol I. Dordrecht: Reidel, 125–162.Google Scholar
Harsanyi, J., and Selten, R. (1988), A General Theory of Equilibrium Selection in Games. Cambridge, MA: MIT Press.Google Scholar
Horgan, T. ([1981] 1985), “Counterfactuals and Newcomb’s Problem”, in Campbell, R. and Sowden, L. (eds.), Paradoxes of Rationality and Cooperation. Vancouver: University of British Columbia Press, 159–182. Originally published in Journal of Philosophy 78:331–356.Google Scholar
Hubin, D., and Ross, G. (1985), “Newcomb’s Perfect Predictor”, Newcomb’s Perfect Predictor 19:439–446.Google Scholar
Hurley, S. L. (1991), “Newcomb’s Problem, Prisoners’ Dilemma, and Collective Action”, Newcomb’s Problem, Prisoners’ Dilemma, and Collective Action 86:173–196.Google Scholar
Jeffrey, R. (1983), The Logic of Decision, 2nd ed. Chicago: University of Chicago Press.Google Scholar
Joyce, James (1999), The Foundations of Causal Decision Theory. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kreps, D. M., Milgrom, P., Roberts, J., and Wilson, R. (1982), “Rational Cooperation in the Finitely Repeated Prisoners’ Dilemma”, Rational Cooperation in the Finitely Repeated Prisoners’ Dilemma 27:245–252.Google Scholar
Levi, I. (1978), “Newcomb’s Many Problems”, in Hooker, C., Leach, J. and McClennen, E. (eds.), Foundations and Applications of Decision Theory. Dordrecht: Reidel, 369–383.CrossRefGoogle Scholar
Levi, I. (1982), “A Note on Newcombmania”, A Note on Newcombmania 79:337–342.Google Scholar
Levi, I. (2000), “Review of James Joyce: The Foundations of Causal Decision Theory”, Review of James Joyce: The Foundations of Causal Decision Theory 97:387–402.Google Scholar
Lewis, D. ([1979] 1885), “Prisoner’s Dilemma Is a Newcomb’s Problem”, in Campbell, R. and Sowden, L. (eds.), Paradoxes of Rationality and Cooperation. Vancouver: University of British Columbia Press, 251–255. Originally published in Philosophy and Public Affairs 8:235–240.Google Scholar
Lewis, D. ([1981] 1988), “Causal Decision Theory”, in Gärdenfors, P. and Sahlin, N.-E. (eds.), Decision, Probability and Utility. Cambridge: Cambridge University Press, 377–405. Originally published in Australasian Journal of Philosophy 59:5–30.CrossRefGoogle Scholar
Mackie, J. L. (1977), “Newcomb’s Problem and the Direction of Causation”, in Mackie, J. L., Logic and Knowledge, Selected Papers, Vol. I. Oxford: Clarendon, 145–158. Originally published in Canadian Journal of Philosophy 7:213–225.Google Scholar
Nozick, R. ([1969] 1985), “Newcomb’s Problem and Two Principles of Choice”, abridged in Campbell, R. and Sowden, L. (eds.), Paradoxes of Rationality and Cooperation. Vancouver: University of British Columbia Press, 107–133. Originally published in N. Rescher (ed.), Essays in Honor of Carl G. Hempel. Dordrecht: Reidel, 114–146.Google Scholar
Pearl, J. (2000), Causality: Models, Reasoning, and Inference. Cambridge: Cambridge University Press.Google Scholar
Price, H. (1986), “Against Causal Decision Theory”, Against Causal Decision Theory 67:195–212.Google Scholar
Price, H. (1991), “Agency and Probabilistic Causality”, Agency and Probabilistic Causality 42:157–176.Google Scholar
Rapoport, A. (1966), Two-Person Game Theory. Ann Arbor: University of Michigan Press.Google Scholar
Routledge, B. R. (1998), “Economics of the Prisoner’s Dilemma: A Background”, in Danielson, P. A. (ed.), Modelling Rationality, Morality, and Evolution, Vancouver Studies in Cognitive Science, vol. 7. Oxford: Oxford University Press, 92–118.Google Scholar
Sobel, J. H. (1985), “Not Every Prisoner’s Dilemma Is a Newcomb Problem”, in Campbell, R. and Sowden, L. (eds.), Paradoxes of Rationality and Cooperation. Vancouver: University of British Columbia Press, 263–274.Google Scholar
Sobel, J. H. (1988), “Infallible Predictors”, Infallible Predictors 97:3–24.Google Scholar
Sobel, J. H. (1991), “Some Versions of Newcomb’s Problem Are Prisoners’ Dilemmas”, Some Versions of Newcomb’s Problem Are Prisoners’ Dilemmas 86:197–208.Google Scholar
Sorensen, R. A. (1985), “The Iterated Versions of Newcomb’s Problem and the Prisoner’s Dilemma”, The Iterated Versions of Newcomb’s Problem and the Prisoner’s Dilemma 63:157–166.Google Scholar