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A mathematical theory of power

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  • Daniele De Luca

Abstract

This paper proposes a new approach to power in Game Theory. Cooperation and conflict are simulated with a mechanism of payoff alteration, called F-game. Using convex combinations of preferences, an F-game can measure players' attitude to cooperate. We can then define actual and potential power as special relations between different states of the system.

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  • Daniele De Luca, 2024. "A mathematical theory of power," Papers 2401.16406, arXiv.org.
  • Handle: RePEc:arx:papers:2401.16406
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    References listed on IDEAS

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    1. John A. List, 2009. "Social Preferences: Some Thoughts from the Field," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 563-583, May.
    2. Jaime Simão Sichman, 1998. "DEPINT: Dependence-Based Coalition Formation in an Open Multi-Agent Scenario," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 1(2), pages 1-3.
    3. Harald Wiese, 2009. "Applying cooperative game theory to power relations," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(4), pages 519-533, July.
    4. Pranab Bardhan, 1991. "On The Concept Of Power In Economics," Economics and Politics, Wiley Blackwell, vol. 3(3), pages 265-277, November.
    5. Ernst Fehr & Gary Charness, 2023. "Social Preferences: Fundamental Characteristics and Economic Consequences," CESifo Working Paper Series 10488, CESifo.
    6. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    7. Ken Binmore, 2010. "Social norms or social preferences?," Mind & Society: Cognitive Studies in Economics and Social Sciences, Springer;Fondazione Rosselli, vol. 9(2), pages 139-157, December.
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