Abstract
This paper does not deal with the applications of game theory for which this theory was first developed, that is, for modelling economic systems and rational decision making. But I do not want to consider games as abstract mathematical structures, either. I want to concentrate on what it is that makes a game actually playable. This playability means both the possibility of finding and formulating the strategy that a player uses and the feasibility of actually applying the strategy in question in making one’s moves.
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Notes
See my paper, “Paradigms for Language Theory”, in: Acta Philosophica Fennica,49, 1990, pp. 181–209.
See Jaakko Hintikka/Gabriel Sandu, “Game-Theoretical Semantics”, in: Johan van Benthem/Alice terMeulen (Eds.), Handbook of Logic and Language. Amsterdam: Elsevier 1997, pp. 361–410.
Cf. here Merrill B. Hintikka/Jaakko Hintikka, Investigating Wittgenstein. Oxford: Basil Blackwell 1986.
John von Neumann, “Zur Theorie der Gesellschaftsspiele”, in: Mathematische Annalen,100, 1928, pp. 295–320; cf. his “Communication on the Borel Notes”, in: Econometrica,21, 1953, pp. 124–125.
See Risto Hilpinen, “On C.S. Peirce’s Theory of Proposition: Peirce as a Precursor of Game-theoretical Semantics”, in: E. Freeman (Ed.), The Relevance of Charles S. Peirce, La Salle, Illinois: The Hegeler Institute 1983, pp. 264–270.
Cf. Jaakko Hintikka, The Princtples of Mathematics Revisited. Cambridge: Cambridge University Press 1996, ch. 7.
See op. cit.,Chapters 3–4.
See op. cit., Chapters 4 and 6.
See Eric van Damme, “Extensive Form games”, in: John Eatwell et al. (Eds.), The New Palgrave: Game Theory,,New York: W.W. Norton 1989, pp.139–148, especially p. 143, where further information is provided about the relationship between the extensive and the normal form.
Ken Binmore, “Modelling Rational Players, Part I”, in: Economics and Philosophy vol. 3, 1987, pp. 179–214, especially p. 189.
This is the most general gambit used to disparage the general theoretical interest of independence-friendly logic. It backfires on its users, however, for independence-friendly logic can be obtained from ordinary first-order logic by merely relaxing the use of parentheses. See my paper “No Scope for Scope?”, forthcoming.
See here op. cit.,Note 6 above, Chapter 8.
Here and in the following, see op. cit.,Chapter 10.
Michael Rabin, “Effective Computability of Winning Strategies”, in: M. Dresher et al. (Eds.), Contributions to the Theory of Games III. Princeton University Press 1957, pp. 147–157.
James P. Jones, “Recursive Undecidability - An Exposition”, in: The American Mathematical Monthly,81, 1974, pp. 359–367.
Cf. e.g., Yuri V. Matiyasevich, Hilbert’s Tenth Problem. Cambridge, MA: MIT Press 1993.
See op. cit., Chapter 11.
Op. cit., Chapter 10.
See Jaakko Hintikka/Arto Mutanen, “An Alternative Concept of Computability”, forthcoming.
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Hintikka, J. (1998). A Game Theory of Logic — A Logic of Game Theory. In: Leinfellner, W., Köhler, E. (eds) Game Theory, Experience, Rationality. Vienna Circle Institute Yearbook [1997], vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1654-3_25
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