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Avoiding the curse of dimensionality in dynamic stochastic games

  • Ulrich Doraszelski
  • Kenneth L. Judd

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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Article provided by Econometric Society in its journal Quantitative Economics.

Volume (Year): 3 (2012)
Issue (Month): 1 (03)
Pages: 53-93

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Handle: RePEc:ecm:quante:v:3:y:2012:i:1:p:53-93
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  1. Ulrich Doraszelski & Mark Satterthwaite, 2003. "Foundations of Markov-Perfect Industry Dynamics. Existence, Purification, and Multiplicity," Discussion Papers 1383, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, 06.
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  9. Patricia Langohr, 2003. "Competitive Convergence and Divergence: Capability and Position Dynamics," Computing in Economics and Finance 2003 229, Society for Computational Economics.
  10. Ulrich Doraszelski & Sarit Markovich, 2004. "Advertising Dynamics and Competitive Advantage," Econometric Society 2004 North American Summer Meetings 162, Econometric Society.
  11. Erkan Erdem & James Tybout, 2003. "Trade Policy and Industrial Sector Responses: Using Evolutionary Models to Interpret the Evidence," NBER Working Papers 9947, National Bureau of Economic Research, Inc.
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  13. 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.
  14. Ulrich Doraszelski & Sarit Markovich, 2004. "Advertising Dynamics and Competitive Advantage," Computing in Economics and Finance 2004 61, Society for Computational Economics.
  15. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  16. 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.
  17. repec:cup:cbooks:9780521637329 is not listed on IDEAS
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