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Avoiding the Curse of Dimensionality in Dynamic Stochastic Games

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  • Ulrich Doraszelski
  • Kenneth L. Judd

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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Bibliographic Info

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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  1. 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.
  2. Andrew Caplin & Barry Nalebuff, 1990. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Cowles Foundation Discussion Papers 937, Cowles Foundation for Research in Economics, Yale University.
  3. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711.
  4. C. Lanier Benkard, 2004. "A Dynamic Analysis of the Market for Wide-Bodied Commercial Aircraft," Review of Economic Studies, Wiley Blackwell, vol. 71, pages 581-611, 07.
  5. Ulrich Doraszelski & Sarit Markovich, 2004. "Advertising Dynamics and Competitive Advantage," Econometric Society 2004 North American Summer Meetings 162, Econometric Society.
  6. Martin Pesendorfer & Philipp Schmidt-Dengler, 2003. "Identification and Estimation of Dynamic Games," NBER Working Papers 9726, National Bureau of Economic Research, Inc.
  7. Ronald L. Goettler & Christine A. Parlour, 2004. "Equilibrium in a Dynamic Limit Order Market," 2004 Meeting Papers 757, Society for Economic Dynamics.
  8. Ariel Pakes, 2000. "A Framework for Applied Dynamic Analysis in I.O," NBER Working Papers 8024, National Bureau of Economic Research, Inc.
  9. Jonathan Levin (Stanford University) & Pat Bajari & Lanier Benkard, 2004. "Estimating Dynamic Models of Imperfect Competition," Econometric Society 2004 North American Winter Meetings 627, Econometric Society.
  10. 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.
  11. Patricia Langohr, 2003. "Competitive Convergence and Divergence: Capability and Position Dynamics," Computing in Economics and Finance 2003 229, Society for Computational Economics.
  12. Ericson, Richard & Pakes, Ariel, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Wiley Blackwell, vol. 62(1), pages 53-82, January.
  13. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, October.
  14. 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.
  15. Ulrich Doraszelski & Sarit Markovich, 2004. "Advertising Dynamics and Competitive Advantage," Computing in Economics and Finance 2004 61, Society for Computational Economics.
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Cited by:
  1. Juan Carlos Parra-Alvarez, 2013. "A comparison of numerical methods for the solution of continuous-time DSGE models," CREATES Research Papers 2013-39, School of Economics and Management, University of Aarhus.
  2. C. Lanier Benkard & Przemyslaw Jeziorski & Gabriel Y. Weintraub, 2013. "Oblivious Equilibrium for Concentrated Industries," NBER Working Papers 19307, National Bureau of Economic Research, Inc.
  3. 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.
  4. Peter Arcidiacono & Patrick Bayer & Jason R. Blevins & Paul B. Ellickson, 2012. "Estimation of Dynamic Discrete Choice Models in Continuous Time with an Application to Retail Competition," NBER Working Papers 18449, National Bureau of Economic Research, Inc.
  5. Pichler, Paul, 2011. "Solving the multi-country Real Business Cycle model using a monomial rule Galerkin method," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 240-251, February.

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