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Price of anarchy in a linear-state stochastic dynamic game

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  • Parilina, Elena
  • Sedakov, Artem
  • Zaccour, Georges

Abstract

We consider a linear-state dynamic game played over an event tree and determine analytically the price of anarchy (PoA), which is given by the ratio of player’s outcome in the cooperative game to her outcome in the noncooperative game. Next, we illustrate our findings in the context of a pollution control problem. We conduct a sensitivity analysis to assess the impact on PoA, and its lower and upper bounds, of varying the different parameter values.

Suggested Citation

  • Parilina, Elena & Sedakov, Artem & Zaccour, Georges, 2017. "Price of anarchy in a linear-state stochastic dynamic game," European Journal of Operational Research, Elsevier, vol. 258(2), pages 790-800.
    • Handle: RePEc:eee:ejores:v:258:y:2017:i:2:p:790-800
    DOI: 10.1016/j.ejor.2016.09.025
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    References listed on IDEAS

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    1. Genc, Talat S. & Reynolds, Stanley S. & Sen, Suvrajeet, 2007. "Dynamic oligopolistic games under uncertainty: A stochastic programming approach," Journal of Economic Dynamics and Control, Elsevier, vol. 31(1), pages 55-80, January.
    2. Pierre-Olivier Pineau & Pauli Murto, 2003. "An Oligopolistic Investment Model of the Finnish Electricity Market," Annals of Operations Research, Springer, vol. 121(1), pages 123-148, July.
    3. Van Long, Ngo, 2012. "Applications of Dynamic Games to Global and Transboundary Environmental Issues: A Review of the Literature," Strategic Behavior and the Environment, now publishers, vol. 2(1), pages 1-59, January.
    4. Steffen Jørgensen & Georges Zaccour, 2007. "Developments in differential game theory and numerical methods: economic and management applications," Computational Management Science, Springer, vol. 4(2), pages 159-181, April.
    5. Victor Martínez-de-Albéniz & David Simchi-Levi, 2009. "Competition in the Supply Option Market," Operations Research, INFORMS, vol. 57(5), pages 1082-1097, October.
    6. Ingene, Charles A. & Taboubi, Sihem & Zaccour, Georges, 2012. "Game-Theoretic Coordination Mechanisms in Distribution Channels: Integration and Extensions for Models Without Competition," Journal of Retailing, Elsevier, vol. 88(4), pages 476-496.
    7. Amr Farahat & Georgia Perakis, 2011. "TECHNICAL NOTE---A Comparison of Bertrand and Cournot Profits in Oligopolies with Differentiated Products," Operations Research, INFORMS, vol. 59(2), pages 507-513, April.
    8. Genc, Talat S. & Sen, Suvrajeet, 2008. "An analysis of capacity and price trajectories for the Ontario electricity market using dynamic Nash equilibrium under uncertainty," Energy Economics, Elsevier, vol. 30(1), pages 173-191, January.
    9. Pineau, Pierre-Olivier & Rasata, Hasina & Zaccour, Georges, 2011. "Impact of some parameters on investments in oligopolistic electricity markets," European Journal of Operational Research, Elsevier, vol. 213(1), pages 180-195, August.
    10. Georgia Perakis & Guillaume Roels, 2007. "The Price of Anarchy in Supply Chains: Quantifying the Efficiency of Price-Only Contracts," Management Science, INFORMS, vol. 53(8), pages 1249-1268, August.
    11. Tamer Başar & Quanyan Zhu, 2011. "Prices of Anarchy, Information, and Cooperation in Differential Games," Dynamic Games and Applications, Springer, vol. 1(1), pages 50-73, March.
    12. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2007. "Fast, Fair, and Efficient Flows in Networks," Operations Research, INFORMS, vol. 55(2), pages 215-225, April.
    13. Roughgarden, Tim & Schoppmann, Florian, 2015. "Local smoothness and the price of anarchy in splittable congestion games," Journal of Economic Theory, Elsevier, vol. 156(C), pages 317-342.
    14. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2004. "Selfish Routing in Capacitated Networks," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 961-976, November.
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    Cited by:

    1. Sedakov, Artem & Qiao, Han & Wang, Shouyang, 2021. "A model of river pollution as a dynamic game with network externalities," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1136-1153.
    2. Parilina, Elena M. & Zaccour, Georges, 2024. "Payment schemes for sustaining cooperation in dynamic games played over event trees," European Journal of Operational Research, Elsevier, vol. 313(3), pages 1200-1216.
    3. Cao, Yiyin & Dang, Chuangyin & Xiao, Zhongdong, 2022. "A differentiable path-following method to compute subgame perfect equilibria in stationary strategies in robust stochastic games and its applications," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1032-1050.
    4. Kameda, Hisao, 2021. "Magnitude of inefficiency," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1133-1145.

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