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Avoiding the Curse of Dimensionality in Dynamic Stochastic Games

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Ulrich Doraszelski
Kenneth L. Judd

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Abstract

Discrete-time stochastic games with a finite number of states have been widely ap- plied to study the strategic interactions among forward-looking players in dynamic en- vironments. However, these games suffer from a "curse of dimensionality" since the cost of computing players' expectations over all possible future states increases exponentially in the number of state variables. We explore the alternative of continuous-time stochas- tic games with a finite number of states, and show that continuous time has substantial computational and conceptual advantages. Most important, continuous time avoids the curse of dimensionality, thereby speeding up the computations by orders of magnitude in games with more than a few state variables. Overall, the continuous-time approach opens the way to analyze more complex and realistic stochastic games than currently feasible.

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Paper provided by Harvard - Institute of Economic Research in its series Harvard Institute of Economic Research Working Papers with number 2059.

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Date of creation: 2005
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Handle: RePEc:fth:harver:2059

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Ronald L. Goettler & Christine A. Parlour, 2004. "Equilibrium in a Dynamic Limit Order Market," 2004 Meeting Papers 757, Society for Economic Dynamics.
  2. J. Levin & P. Bajari, 2004. "Estimating Dynamic Models of Imperfect Competition," 2004 Meeting Papers 579, Society for Economic Dynamics. [Downloadable!]
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  3. Pesendorfer, Martin & Schmidt-Dengler, Philipp, 2003. "Identification and Estimation of Dynamic Games," CEPR Discussion Papers 3965, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  4. C. Lanier Benkard, 2004. "A Dynamic Analysis of the Market for Wide-Bodied Commercial Aircraft," Review of Economic Studies, Blackwell Publishing, vol. 71, pages 581-611, 07. [Downloadable!] (restricted)
  5. Chaim Fershtman & Ariel Pakes, 2000. "A Dynamic Oligopoly with Collusion and Price Wars," RAND Journal of Economics, The RAND Corporation, vol. 31(2), pages 207-236, Summer.
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  6. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January. [Downloadable!] (restricted)
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  7. Ericson, Richard & Pakes, Ariel, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Blackwell Publishing, vol. 62(1), pages 53-82, January. [Downloadable!] (restricted)
  8. Ariel Pakes & Michael Ostrovsky & Steve Berry, 2004. "Simple Estimators for the Parameters of Discrete Dynamic Games (with Entry/Exit Examples)," Harvard Institute of Economic Research Working Papers 2036, Harvard - Institute of Economic Research. [Downloadable!]
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  9. Ulrich Doraszelski & Sarit Markovich, 2004. "Advertising Dynamics and Competitive Advantage," Computing in Economics and Finance 2004 61, Society for Computational Economics. [Downloadable!]
  10. David Besanko & Ulrich Doraszelski, 2004. "Capacity Dynamics and Endogenous Asymmetries in Firm Size," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 23-49, Spring.
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  11. Pakes, Ariel & McGuire, Paul, 2001. "Stochastic Algorithms, Symmetric Markov Perfect Equilibrium, and the 'Curse' of Dimensionality," Econometrica, Econometric Society, vol. 69(5), pages 1261-81, September.
  12. Ulrich Doraszelski & Sarit Markovich, 2004. "Advertising Dynamics and Competitive Advantage," Econometric Society 2004 North American Summer Meetings 162, Econometric Society. [Downloadable!]
  13. Patricia Langohr, 2003. "Competitive Convergence and Divergence: Capability and Position Dynamics," Computing in Economics and Finance 2003 229, Society for Computational Economics.
  14. Ariel Pakes & Paul McGuire, 1994. "Computing Markov-Perfect Nash Equilibria: Numerical Implications of a Dynamic Differentiated Product Model," RAND Journal of Economics, The RAND Corporation, vol. 25(4), pages 555-589, Winter. [Downloadable!] (restricted)
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  15. Gowrisankaran, Gautam, 1999. "Efficient representation of state spaces for some dynamic models," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1077-1098, August. [Downloadable!] (restricted)
  16. Ariel Pakes, 2000. "A Framework for Applied Dynamic Analysis in I.O," NBER Working Papers 8024, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  1. Besanko, David & Doraszelski, Ulrich & Kryukov, Yaroslav & Satterthwaite, Mark, 2007. "Learning-by-Doing, Organizational Forgetting and Industry Dynamics," CEPR Discussion Papers 6160, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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