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Rational beliefs in extensive games

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Abstract

Given an extensive game, with every node x and every player i a subset k i (x) of the set of terminal nodes is associated, and is given the interpretation of player i's knowledge (or information) at node x. A belief of player i is a function that associates with every node x an element of the set K i (x). A belief system is an n-tuple of beliefs, one for each player. A belief system is rational if it satisfies some natural consistency properties. The main result of the paper is that the notion of rational belief system gives rise to a refinement of the notion of subgame-perfect equilibrium.

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References

  • Bonanno, G.: 1990, ‘Knowledge and beliefs in extensive games,’ Department of Economics Working Paper No. 361, University of California, Davis.

    Google Scholar 

  • Bonanno, G.: 1991, ‘Players' information in extensive games,’ to appear in: Mathematical Social Sciences.

  • Greenberg, J.: 1990, The Theory of Social Situations, Cambridge University Press, Cambridge.

    Google Scholar 

  • Kreps, D. and Wilson, R.: 1982, ‘Sequential equilibria,’ Econometrica, 50, 863–894.

    Google Scholar 

  • Selten, R.: 1965, ‘Spieltheoretische Behandlung eines Oligopolmodells mit Nachfrägetragheit,’ Zeitschrift für die gesamte Staatswissenschaft, 12, 301–324 and 667–689.

    Google Scholar 

  • Selten, R.: 1973, ‘A simple model of imperfect competition where 4 are few and 6 are many,’ International Journal of Game Theory, 2, 141–201.

    Google Scholar 

  • Selten, R.: 1975, ‘Re-examination of the perfectness concept for equilibrium points in extensive games,’ International Journal of Game Theory, 4, 25–55.

    Google Scholar 

  • Zermelo, E.: 1912, Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels, Proceedings, Fifth International Congress of Mathematicians, Vol. 2, pp. 501–504.

    Google Scholar 

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Authors and Affiliations

  1. Department of Economics, University of California, 95616, Davis, CA, USA

    Giacomo Bonanno

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  1. Giacomo Bonanno
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Bonanno, G. Rational beliefs in extensive games. Theor Decis 33, 153–176 (1992). https://doi.org/10.1007/BF00134094

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  • DOI: https://doi.org/10.1007/BF00134094

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