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Knowledge, Belief and Counterfactual Reasoning in Games

  • Robert Stalnaker (a1)
Abstract

Deliberation about what to do in any context requires reasoning about what will or would happen in various alternative situations, including situations that the agent knows will never in fact be realized. In contexts that involve two or more agents who have to take account of each others' deliberation, the counterfactual reasoning may become quite complex. When I deliberate, I have to consider not only what the causal effects would be of alternative choices that I might make, but also what other agents might believe about the potential effects of my choices, and how their alternative possible actions might affect my beliefs. Counterfactual possibilities are implicit in the models that game theorists and decision theorists have developed – in the alternative branches in the trees that model extensive form games and the different cells of the matrices of strategic form representations – but much of the reasoning about those possibilities remains in the informal commentary on and motivation for the models developed. Puzzlement is sometimes expressed by game theorists about the relevance of what happens in a game ‘off the equilibrium path’: of what would happen if what is (according to the theory) both true and known by the players to be true were instead false.

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Adams E. 1970. ‘Subjunctive and indicative conditionals’. Foundations of Language, 6
Alchourón C. and Makinson D.. 1982. ‘The logic of theory change: contraction functions and their associated revision functions’. Theoria, 48:1437
Alchourón C., Gärdenfors P. and Makinson D.. 1985. ‘On the logic of theory change: partial meet functions for contraction and revision’. Journal of Symbolic Logic, 50:510–30
Aumann R. 1976. ‘Agreeing to Disagree’. Annals of Statistics, 4:1236–39
Bacharach M. 1985. ‘Some extensions of a claim of Aumann in an axiomatic model of knowledge’. Journal of Economic Theory, 37:167–90
Bernheim B. 1984. ‘Rationalizable strategic behavior’. Econometrica, 52:1007–28
Blume L., Brandenburger A. and Dekel E.. 1991a. ‘Lexicographic probabilities and choice under uncertainty’. Econometrica, 59:6179
Blume L., Brandenburger A. and Dekel E.. 1991b. ‘Lexicographic probabilities and equilibrium refinements’. Econometrica, 59:8198
Dekel E. and Fudenberg D.. 1990. ‘Rational behavior with payoff uncertainty’. Journal of Economic Theory, 52:243–67
Fudenberg D. and Tirole J.. 1992. Game Theory. The MIT Press
Gärdenfors P. 1988. Knowledge in Flux: Modeling the Dynamics of Epistemic States. MIT Press
Gibbard A. and Harper W.. 1981. ‘Counterfactuals and two kinds of expected utility,’ in Foundations and Applications of Decision Theory. Hooker C. et al. , (eds.). Reidel
Grove A. 1988. ‘Two modelings for theory change’. Journal of Philosophical Logic, 17:157–70
Harper W. 1975. ‘Rational belief change, popper functions and counterfactuals’. Synthese, 30:221–62
Makinson D. 1985. ‘How to give it up: a survey of some formal aspects of the logic of theory change’. Synthese, 62:347–63
Mongin P. 1994. ‘The logic of belief change and nonadditive probability’, in Logic and Philosophy of Science in Uppsala. Prawitz D. and Westerstahl D. (eds.). Kluwer
Lewis D. 1980. ‘Causal decision theory’. Australasian Journal of Philosophy, 59:530
Pappas G. and Swain M. (eds.). 1978. Essays on Knowledge and Justification. Cornell University Press
Pearce G. 1984. ‘Rationalizable strategic behavior and the problem of perfection’. Econometrica, 52:1029–50
Pettit P. and Sugden R.. 1989. ‘The backward induction paradox’. Journal of Philosophy, 86:169–82
Spohn W. 1987. ‘Ordinal conditional functions: a dynamic theory of epistemic states’. In Causation in Decision, Belief Change and Statistics. Harper W. and Skyrms B. (eds.). Reidel, 2:105–34
Skyrms B. 1982. ‘Causal decision theory’. Journal of Philosophy, 79:695711
Skyrms B. 1992. The Dynamics of Rational Deliberation. Harvard University Press
Stalnaker R. 1994. ‘On the evaluation of solution concepts’. Theory and Decision, 37:4973
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Economics & Philosophy
  • ISSN: 0266-2671
  • EISSN: 1474-0028
  • URL: /core/journals/economics-and-philosophy
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