An extension of a theorem of von Neumann and Morgenstern with an application to social choice theory.

*(English)*Zbl 0966.91030Summary: We present an analytical framework and an axiomatic theory of behavior under risk that constitutes an extension of the theory of von Neumann and Morgenstern. The extension entails a relaxation of the mixture space structure of the decision set and requires the restriction of the independence axiom of expected utility theory. We begin with an application to social choice theory which yields an extension of Harsanyi’s impartial observer theorem to the case in which individual preferences do not necessarily satisfy the axioms of expected utility theory. An application to game theory is also discussed.

PDF
BibTeX
XML
Cite

\textit{E. Karni} and \textit{Z. Safra}, J. Math. Econ. 34, No. 3, 315--327 (2000; Zbl 0966.91030)

Full Text:
DOI

##### References:

[1] | Anscombe, F.; Aumann, R., A definition of subjective probability, Annals of mathematical statistics, 34, 199-205, (1963) · Zbl 0114.07204 |

[2] | Crawford, V.P., Equilibrium without independence, Journal of economic theory, 50, 127-154, (1990) · Zbl 0689.90075 |

[3] | Dekel, E.; Safra, Z.; Segal, U., Existence and dynamic consistency of Nash equilibrium with non-expected utility preferences, Journal of economic theory, 55, 229-246, (1991) · Zbl 0749.90091 |

[4] | Diamond, P.A., Cardinal welfare, individualistic ethics, and interpersonal comparison of utility: comment, Journal of political economy, 75, 765-766, (1967) |

[5] | Dow, J.; Werlang, S.R.C., Nash equilibrium under Knightian uncertainty: breaking down backward induction, Journal of economic theory, 64, 305-324, (1994) · Zbl 0813.90132 |

[6] | Fishburn, P.C., Foundations of expected utility, (1982), Reidel Dordrecht, The Netherlands · Zbl 0497.90001 |

[7] | Harsanyi, J.C., Cardinal utility in welfare economics, Journal of political economy, 61, 434-435, (1953) |

[8] | Harsanyi, J.C., Rational behavior and bargaining equilibrium in games and social situations, (1977), Cambridge Univ. Press Cambridge · Zbl 0395.90087 |

[9] | Harsanyi, J.C., Game and decision theoretic models in ethics, () · Zbl 0968.91513 |

[10] | Jaffray, J.-Y., Choice under risk and the security factor: an axiomatic model, Theory and decision, 24, 169-200, (1988) · Zbl 0631.90005 |

[11] | Karni, E., Social welfare functions and fairness, Social choice and welfare, 13, 487-496, (1995) · Zbl 0855.90009 |

[12] | Karni, E. and Safra, Z., 2000. Individual Sense of Justice: A Utility Representation, Mimeo. · Zbl 1103.91336 |

[13] | Karni, E. and Weymark, J.A., 1997. An Informationally Parsimonious Impartial Observer Theorem, Social Choice and Welfare, (forthcoming 1997). · Zbl 1066.91504 |

[14] | Segal, U., Additive separable representations on non-convex sets, Journal of economic theory, 56, 89-99, (1992) · Zbl 0749.90009 |

[15] | Weymark, J.A., A reconsideration of the Harsanyi-Sen debate on utilitarianism, () |

[16] | von Neumann, J.; Morgenstern, O., Theory of games and economic behavior, (1947), Princeton Univ. Press Princeton · Zbl 1241.91002 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.