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An Aversion To Risk Power Index In A Simple Game

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  • Anselme Njocke

    (CATT - Centre d'Analyse Théorique et de Traitement des données économiques - UPPA - Université de Pau et des Pays de l'Adour)

Abstract

In this work, we propose an aversion to risk power index in a simple game based on the precautionary index (or the capacity of influence) of a player in a negotiation, as well as the order in which coalitions are formed. Let us note that some classical power indexes encountered in literature such as the Shapley-Shubik power index (1954), the Johnston index (1978) and the Deegan-Packel power index (1978) are generalized, as it were, by taking risk aversion into account. When submitting the aversion to risk power index to the test of a number of axioms, it appears that the violation of these axioms is strongly linked to the vector of precautionary indexes of the players.We show that in a society exclusively consisting of absolute, timorous players, the aversion to risk power index leads to an equal sharing out of power among its various members, regardless of their marginal contributions.We also show, that when the decision rule is unanimity and when there are only two classes of players, i.e. absolute, timorous players on the one hand, and absolute, courageous players in the other, the aversion to risk power index assigns a zero to each, absolute timorous player, and total power (divided equally) to absolute, courageous players. Eventually we show that a dictator game is akin to a game where the dictator would be the only absolute, courageous player, while all the other players would be absolute, timorous players, whatever the rule of decision requiring a quota strictly greater than the highest individual number of votes, in a simple (or weighted) game.

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  • Anselme Njocke, 2014. "An Aversion To Risk Power Index In A Simple Game," Post-Print hal-05361216, HAL.
    • Handle: RePEc:hal:journl:hal-05361216
    Note: View the original document on HAL open archive server: https://univ-pau.hal.science/hal-05361216v1
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    References listed on IDEAS

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    1. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Edward Packel & John Deegan, 1980. "An axiomated family of power indices for simple n-person games," Public Choice, Springer, vol. 35(2), pages 229-239, January.
    3. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 43-48.
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