David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Theory and Decision 42 (1):53-80 (1997)
In the spatialized Prisoner's Dilemma, players compete against their immediate neighbors and adopt a neighbor's strategy should it prove locally superior. Fields of strategies evolve in the manner of cellular automata (Nowak and May, 1993; Mar and St. Denis, 1993a,b; Grim 1995, 1996). Often a question arises as to what the eventual outcome of an initial spatial configuration of strategies will be: Will a single strategy prove triumphant in the sense of progressively conquering more and more territory without opposition, or will an equilibrium of some small number of strategies emerge? Here it is shown, for finite configurations of Prisoner's Dilemma strategies embedded in a given infinite background, that such questions are formally undecidable: there is no algorithm or effective procedure which, given a specification of a finite configuration, will in all cases tell us whether that configuration will or will not result in progressive conquest by a single strategy when embedded in the given field. The proof introduces undecidability into decision theory in three steps: by (1) outlining a class of abstract machines with familiar undecidability results, by (2) modelling these machines within a particular family of cellular automata, carrying over undecidability results for these, and finally by (3) showing that spatial configurations of Prisoner's Dilemma strategies will take the form of such cellular automata
|Keywords||Undecidability Prisoner's Dilemma cellular automata game theory decision theory computability|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Anthony F. Beavers (2011). Recent Developments in Computing and Philosophy. Journal for General Philosophy of Science 42 (2):385-397.
Similar books and articles
Patrick Grim, Undecidability in the Spatialized Prisoner's Dilemma: Some Philosophical Implications.
Daniel R. Gilbert Jr (1996). The Prisoner's Dilemma and the Prisoners of the Prisoner's Dilemma. Business Ethics Quarterly 6 (2):165-178.
Louis Marinoff (1990). The Inapplicability of Evolutionarily Stable Strategy to the Prisoner's Dilemma. British Journal for the Philosophy of Science 41 (4):461-472.
Charles H. Pence & Lara Buchak (2012). Oyun: A New, Free Program for Iterated Prisoner’s Dilemma Tournaments in the Classroom. Evolution Education and Outreach 5 (3):467-476.
Christopher Stephens (1996). Modelling Reciprocal Altruism. British Journal for the Philosophy of Science 47 (4):533-551.
Toby Ord & Alan Blair, Exploitation and Peacekeeping: Introducing More Sophisticated Interactions to the Iterated Prisoner's Dilemma.
Colin Grant (2004). The Altruists' Dilemma. Business Ethics Quarterly 14 (2):315-328.
Esther Hauk (2003). Multiple Prisoner's Dilemma Games with(Out) an Outside Option: An Experimental Study. Theory and Decision 54 (3):207-229.
Richmond Campbell & Lanning Snowden (eds.) (1985). Paradoxes of Rationality and Cooperation: Prisoner's Dilemma and Newcomb's Problem. University of British Columbia Press.
Elias L. Khalil (2002). Is the Prisoner's Dilemma Metaphor Suitable for Altruism? Distinguishing Self-Control and Commitment From Altruism. Behavioral and Brain Sciences 25 (2):264-265.
John J. Tilley (1994). Accounting for the 'Tragedy' in the Prisoner's Dilemma. Synthese 99 (2):251–76.
Robert Hoffmann (1999). The Independent Localisations of Interaction and Learning in the Repeated Prisoner's Dilemma. Theory and Decision 47 (1):57-72.
Ilan Fischer (2003). The Emergence of Reactive Strategies in Simulated Heterogeneous Populations. Theory and Decision 55 (4):289-314.
Added to index2010-09-02
Total downloads14 ( #115,807 of 1,102,812 )
Recent downloads (6 months)7 ( #36,605 of 1,102,812 )
How can I increase my downloads?