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Stochastic Switching Games and Duopolistic Competition in Emissions Markets

  • Michael Ludkovski
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    We study optimal behavior of energy producers under a CO_2 emission abatement program. We focus on a two-player discrete-time model where each producer is sequentially optimizing her emission and production schedules. The game-theoretic aspect is captured through a reduced-form price-impact model for the CO_2 allowance price. Such duopolistic competition results in a new type of a non-zero-sum stochastic switching game on finite horizon. Existence of game Nash equilibria is established through generalization to randomized switching strategies. No uniqueness is possible and we therefore consider a variety of correlated equilibrium mechanisms. We prove existence of correlated equilibrium points in switching games and give a recursive description of equilibrium game values. A simulation-based algorithm to solve for the game values is constructed and a numerical example is presented.

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    File URL: http://arxiv.org/pdf/1001.3455
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    Paper provided by arXiv.org in its series Papers with number 1001.3455.

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    Date of creation: Jan 2010
    Date of revision: Aug 2010
    Handle: RePEc:arx:papers:1001.3455
    Contact details of provider: Web page: http://arxiv.org/

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    1. Eilon Solan & Nicolas Vieille, 1998. "Correlated Equilibrium in Stochastic Games," Discussion Papers 1226, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Michael Ludkovski, 2008. "Financial Hedging Of Operational Flexibility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(08), pages 799-839.
    3. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-57, April.
    4. R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
    5. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-58, March.
    6. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Economics Papers from University Paris Dauphine 123456789/6019, Paris Dauphine University.
    7. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 1999. "Stopping Games with Randomized Strategies," Discussion Papers 1258, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Andrzej Nowak, 2003. "On a new class of nonzero-sum discounted stochastic games having stationary Nash equilibrium points," International Journal of Game Theory, Springer, vol. 32(1), pages 121-132, December.
    9. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    10. Ramsey, David M. & Szajowski, Krzysztof, 2008. "Selection of a correlated equilibrium in Markov stopping games," European Journal of Operational Research, Elsevier, vol. 184(1), pages 185-206, January.
    11. Laraki, Rida & Solan, Eilon & Vieille, Nicolas, 2005. "Continuous-time games of timing," Journal of Economic Theory, Elsevier, vol. 120(2), pages 206-238, February.
    12. Eran Shmaya & Eilon Solan, 2002. "Two Player Non Zero-Sum Stopping Games in Discrete Time," Discussion Papers 1347, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. Rene Carmona & Michael Ludkovski, 2008. "Pricing Asset Scheduling Flexibility using Optimal Switching," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(5-6), pages 405-447.
    14. Eilon Solan & Nicolas Vieille, 1998. "Quitting Games," Discussion Papers 1227, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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