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Strategy Constrained by Cognitive Limits, and the Rationality of Belief-Revision Policies

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  • Ashton T. Sperry-Taylor

    (National Coalition of Independent Scholars; Ronin Institute; Lititz, PA 17543, USA)

Abstract

Strategy is formally defined as a complete plan of action for every contingency in a game. Ideal agents can evaluate every contingency. But real people cannot do so, and require a belief-revision policy to guide their choices in unforeseen contingencies. The objects of belief-revision policies are beliefs, not strategies and acts. Thus, the rationality of belief-revision policies is subject to Bayesian epistemology. The components of any belief-revision policy are credences constrained by the probability axioms, by conditionalization, and by the principles of indifference and of regularity. The principle of indifference states that an agent updates his credences proportionally to the evidence, and no more. The principle of regularity states that an agent assigns contingent propositions a positive (but uncertain) credence. The result is rational constraints on real people’s credences that account for their uncertainty. Nonetheless, there is the open problem of non-evidential components that affect people’s credence distributions, despite the rational constraint on those credences. One non-evidential component is people’s temperaments, which affect people’s evaluation of evidence. The result is there might not be a proper recommendation of a strategy profile for a game (in terms of a solution concept), despite agents’ beliefs and corresponding acts being rational.

Suggested Citation

  • Ashton T. Sperry-Taylor, 2017. "Strategy Constrained by Cognitive Limits, and the Rationality of Belief-Revision Policies," Games, MDPI, vol. 8(1), pages 1-13, January.
    • Handle: RePEc:gam:jgames:v:8:y:2017:i:1:p:3-:d:86781
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    References listed on IDEAS

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    1. Aumann, Robert J., 1996. "Reply to Binmore," Games and Economic Behavior, Elsevier, vol. 17(1), pages 138-146, November.
    2. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-391, June.
    3. Cubitt, Robin P. & Sugden, Robert, 2003. "Common Knowledge, Salience And Convention: A Reconstruction Of David Lewis' Game Theory," Economics and Philosophy, Cambridge University Press, vol. 19(2), pages 175-210, October.
    4. Cubitt, Robin P. & Sugden, Robert, 2014. "Common Reasoning In Games: A Lewisian Analysis Of Common Knowledge Of Rationality," Economics and Philosophy, Cambridge University Press, vol. 30(3), pages 285-329, November.
    5. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868.
    6. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(2), pages 133-163, October.
    7. Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
    8. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
    9. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(2), pages 179-214, October.
    10. Aumann, Robert J., 1998. "On the Centipede Game," Games and Economic Behavior, Elsevier, vol. 23(1), pages 97-105, April.
    11. Gerd Gigerenzer & Reinhard Selten (ed.), 2002. "Bounded Rationality: The Adaptive Toolbox," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262571641, April.
    12. Binmore, K G, 1985. "Equilibria in Extensive Games," Economic Journal, Royal Economic Society, vol. 95(380a), pages 51-59, Supplemen.
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    Cited by:

    1. Paul Weirich, 2017. "Epistemic Game Theory and Logic: Introduction," Games, MDPI, vol. 8(2), pages 1-3, March.

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