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Newcomb's Problem and Repeated Prisoners’ Dilemmas

Published online by Cambridge University Press:  01 January 2022

Christoph Schmidt-Petri
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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

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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.

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