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Un Indice De Pouvoir D’Aversion Au Risque Dans Un Jeu Simple

Author

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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

Nous proposons, dans ce travail, un indice de pouvoir d'aversion au risque fondé sur l'indice de prudence (ou la capacité d'influence) d'un joueur dans une négociation, et sur l'ordre de formation des coalitions. Il apparaîtra que l'indice de pouvoir d'aversion au risque dans un jeu simple généralise, d'une certaine manière, certains indices de pouvoir classiques rencontrés dans la littérature tels que l'indice de pouvoir de Shapley-Shubik (1954), l'indice de Johnston (1978) et l'indice de Deegan-Packel (1978). En soumettant l'indice de pouvoir d'aversion au risque à l'épreuve d'un certain nombre d'axiomes, il apparaîtra que sa violation, ou sa non violation de ces axiomes est fortement liée au vecteur d'indices de prudence des joueurs. Nous montrons, aussi que, dans une société constituée exclusivement de membres timorés absolus, l'indice de pouvoir d'aversion au risque conduit à un partage égalitaire du pouvoir entre ses différents membres, quelles que soient leurs contributions marginales. Nous montrons de même que, lorsque la règle de décision est l'unanimité, et qu'il n'existe que deux classes de joueurs, les timorés absolus, d'une part, et les vaillants absolus d'autre part, l'indice de pouvoir d'aversion au risque attribue un pouvoir nul à chaque joueur timoré absolu, et la totalité du pouvoir (répartie de manière égalitaire) aux joueurs vaillants. Nous montrons enfin que le jeu dictatorial s'apparente à un jeu où le dictateur serait le seul joueur vaillant absolu, pendant que tous les autres joueurs seraient des timorés absolus, et ce quelle que soit la règle de décision nécessitant un quota strictement supérieur à l'apport individuel en voix (ou en poids) le plus élevé dans un jeu simple (ou pondéré).

Suggested Citation

  • Anselme Njocke, 2014. "Un Indice De Pouvoir D’Aversion Au Risque Dans Un Jeu Simple," Post-Print hal-01885288, HAL.
    • Handle: RePEc:hal:journl:hal-01885288
    Note: View the original document on HAL open archive server: https://univ-pau.hal.science/hal-01885288v2
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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).
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    4. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    5. 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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