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Forecast Horizon for a Class of Dynamic Games

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  • A. Garcia

    (University of Virginia)

Abstract

In theory, a Markov perfect equilibrium of an infinite-horizon nonstationary dynamic game requires from the players the ability to forecast an infinite amount of data. In this paper, we prove that early strategic decisions are decoupled effectively from the tail game in nonstationary dynamic games with discounting and uniformly bounded rewards. This decoupling is formalized by the notion of a forecast horizon. In words, the first-period equilibrium strategies are invariant with respect to changes in the game parameters for periods beyond the forecast horizon. We illustrate our results in the context of dynamic games of exploitation of a common pool resource and make use of the rather natural monotonicity properties of finite-horizon equilibria.

Suggested Citation

  • A. Garcia, 2004. "Forecast Horizon for a Class of Dynamic Games," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 471-486, September.
    • Handle: RePEc:spr:joptap:v:122:y:2004:i:3:d:10.1023_b:jota.0000042591.71156.89
    DOI: 10.1023/B:JOTA.0000042591.71156.89
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    References listed on IDEAS

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    1. Drew Fudenberg & David Levine, 2008. "Subgame–Perfect Equilibria of Finite– and Infinite–Horizon Games," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 1, pages 3-20, World Scientific Publishing Co. Pte. Ltd..
    2. David Levhari & Leonard J. Mirman, 1980. "The Great Fish War: An Example Using a Dynamic Cournot-Nash Solution," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 322-334, Spring.
    3. C. Bes & S. P. Sethi, 1988. "Concepts of Forecast and Decision Horizons: Applications to Dynamic Stochastic Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 295-310, May.
    4. van den Broek, W. A., 2002. "Moving horizon control in dynamic games," Journal of Economic Dynamics and Control, Elsevier, vol. 26(6), pages 937-961, June.
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