Avoiding the curse of dimensionality in dynamic stochastic games

Quantitative Economics

Volumn 3, Issue 1, 2012, Pages 53-93

  Doraszelski, Ulrich ^a   Judd, Kenneth L ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Continuous time; Dynamic stochastic games; Markov perfect equilibrium; Numerical methods

Indexed keywords

EID: 84883532075     PISSN: 17597323     EISSN: 17597331     Source Type: Journal    
DOI: 10.3982/QE153     Document Type: Article

References (55)

1. Arcidiacono, P., P. Bayer, J. Blevins, and P. Ellickson (2010), "Estimation of dynamic discrete choice models in continuous time." Working paper, Duke University, Durham
2. Basar, T. and J. Olsder (1999), Dynamic Noncooperative Game Theory, second edition. Society for Industrial and Applied Mathematics, Philadelphia
3. Bellman, R. (1957), Dynamic Programming. Princeton University Press, Princeton
4. Benkard, L. (2004), "A dynamic analysis of the market for wide-bodied commercial aircraft. Review of Economic Studies, 71 (3), 581-611. DOI: 10.1111/j.1467-937X.2004.00297.x
5. Berry, S. and A. Pakes (1993), "Some applications and limitations of recent advances in empirical industrial organization: Merger analysis. American Economic Review, 83 (2), 247-252.
6. Bertsekas, D. and J. Tsitsiklis (1997), Parallel and Distributed Computation: Numerical Methods. Athena Scientific, Belmont
7. Besanko, D. and U. Doraszelski (2004), "Capacity dynamics and endogenous asymmetries in firm size. Rand Journal of Economics, 35 (1), 23-49. DOI: 10.2307/1593728
8. Besanko, D., U. Doraszelski, Y. Kryukov, and M. Satterthwaite (2010), "Learning-by-doing, organizational forgetting, and industry dynamics. Econometrica, 78 (2), 453-508. DOI: 10.3982/ECTA6994
9. Besanko, D., U. Doraszelski, L. Lu, and M. Satterthwaite (2010a), "Lumpy capacity investment and disinvestment dynamics. Operations Research, 58 (4), 1178-1193. DOI: 10.1287/opre.1100.0823
10. Besanko, D., U. Doraszelski, L. Lu, and M. Satterthwaite (2010b), "On the role of demand and strategic uncertainty in capacity investment and disinvestment dynamics. International Journal of Industrial Organization, 28 (4), 383-389. DOI: 10.1016/j.ijindorg.2010.02.013
11. Borkovsky, R., U. Doraszelski, and Y. Kryukov (2010), "A user's guide to solving dynamic stochastic games using the homotopy method. Operations Research, 58 (4), 1116-1132. DOI: 10.1287/opre.1100.0843
12. Breton, M. (1991), "Algorithms for stochastic games." In Stochastic Games and Related Topics: In Honor of Professor L.S. Shapley (T. Raghavan, T. Ferguson, T. Parthasarathy, and O. Vrieze, eds.), 45-57, Kluwer Academic Publishers, Dordrecht
13. Caplin, A. and B. Nalebuff (1991), "Aggregation and imperfect competition: On the existence of equilibrium. Econometrica, 59 (1), 25-59. DOI: 10.2307/2938239
14. Chen, J. (2009), "The effects of mergers with dynamic capacity accumulation. International Journal of Industrial Organization, 27, 92-109. DOI: 10.1016/j.ijindorg.2008.05.002
15. Chen, J., U. Doraszelski, and J. Harrington (2009), "Avoiding market dominance: Product compatibility in markets with network effects. Rand Journal of Economics, 40 (3), 455-485. DOI: 10.1111/j.1756-2171.2009.00073.x
16. de Roos, N. (2004), "A model of collusion timing. International Journal of Industrial Organization, 22, 351-387. DOI: 10.1016/j.ijindorg.2003.10.003
17. Dockner, E., S. Jorgensen, N. Van Long, and G. Sorger (2000), Differential Games in Economics and Management Science. Cambridge University Press, Cambridge
18. Doraszelski, U. and K. Judd (2007), "Dynamic stochastic games with sequential state-to-state transitions." Working paper, Harvard University, Cambridge
19. Doraszelski, U. and S. Markovich (2007), "Advertising dynamics and competitive advantage. Rand Journal of Economics, 38 (3), 557-592. DOI: 10.1111/j.0741-6261.2007.00101.x
20. Doraszelski, U. and A. Pakes (2007), "A framework for applied dynamic analysis in IO." In Handbook of Industrial Organization, Vol. 3 (M. Armstrong and R. Porter, eds.), 1887-1966, North-Holland, Amsterdam
21. Doraszelski, U. and M. Satterthwaite (2010), "Computable Markov-perfect industry dynamics. Rand Journal of Economics, 41 (2), 215-243. DOI: 10.1111/j.1756-2171.2010.00097.x
22. Elfving, G. (1937), "Zur Theorie der Markoffschen Ketten. Acta Societatis Scientiarum Fennicae Nova Series A, 2 (8), 1-17.
23. Ericson, R. and A. Pakes (1995), "Markov-perfect industry dynamics: A framework for empirical work. Review of Economic Studies, 62, 53-82. DOI: 10.2307/2297841
24. Escobar, J. (2008), "Existence of pure and behavior strategy stationary Markov equilibrium in dynamic stochastic games." Working paper, Stanford University, Stanford
25. Federgruen, A. (1978), "On N-person stochastic games with denumerable state space. Advances in Applied Probability, 10, 452-471. DOI: 10.2307/1426945
26. Feinberg, E. (2004), "Continuous time discounted jump Markov decision processes: A discrete-event approach. Mathematics of Operations Reserach, 29 (3), 492-524. DOI: 10.1287/moor.1040.0089
27. Ferris, M., K. Judd, and K. Schmedders (2007), "Solving dynamic games with Newton's method." Working paper, University of Wisconsin, Madison
28. Fershtman, C. and A. Pakes (2000), "A dynamic oligopoly with collusion and price wars. Rand Journal of Economics, 31, 207-236. DOI: 10.2307/2601038
29. Fershtman, C. and A. Pakes (2011), "Dynamic games with asymmetric information: A framework for empirical work." Working paper, Harvard University, Cambridge
30. Filar, J. and K. Vrieze (1997), Competitive Markov Decision Processes. Springer, New York
31. Fink, A. (1964), "Equilibrium in a stochastic n-person game. Journal of Science of the Hiroshima University Series A-I, 28, 89-93.
32. Gowrisankaran, G. (1999a), "A dynamic model of endogenous horizontal mergers. Rand Journal of Economics, 30 (1), 56-83. DOI: 10.2307/2556046
33. Gowrisankaran, G. (1999b), "Efficient representation of state spaces for some dynamic models. Journal of Economic Dynamics and Control, 23, 1077-1098. DOI: 10.1016/S0165-1889(98)00057-8
34. Herings, J. and R. Peeters (2004), "Stationary equilibria in stochastic games: Structure, selection, and computation. Journal of Economic Theory, 118, 32-60. DOI: 10.1016/j.jet.2003.10.001
35. Howard, R. (1960), Dynamic Programming and Markov Processes. MIT Press, Cambridge
36. Isaacs, R. (1954), Differential Games. John Wiley & Sons, New York
37. Judd, K. (1998), Numerical Methods in Economics. MIT Press, Cambridge
38. Kryukov, Y. (2008), "Dynamic R&D and the effectiveness of policy intervention in the pharmaceutical industry." Working paper, Carnegie Mellon University, Pittsburgh
39. Langohr, P. (2003), "Competitive convergence and divergence: Capability and position dynamics." Working paper, Northwestern University, Evanston
40. Markovich, S. (2008), "Snowball: A dynamic oligopoly model with indirect network effects. Journal of Economic Dynamics and Control, 32, 909-938. DOI: 10.1016/j.jedc.2007.04.005
41. Maskin, E. and J. Tirole (2001), "Markov perfect equilibrium, I: Observable actions. Journal of Economic Theory, 100, 191-219. DOI: 10.1006/jeth.2000.2785
42. Mehra, R. (2003), "The equity premium: Why is it a puzzle? Financial Analysis Journal, 59 (1), 54-69. DOI: 10.2469/faj.v59.n1.2503
43. Mertens, J. (2002), "Stochastic games." In Handbook of Game Theory, Vol. 3 (R. Aumann and S. Hart, eds.), 1810-1832, Elsevier, Amsterdam
44. Ortega, J. and W. Rheinboldt (1970), Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York
45. Pakes, A. (1994), "Dynamic structural models, problems, and prospects: mixed continuous discrete controls and market interactions." In Advances in Econometrics: Sixth World Congress, Vol. 2 (C. Sims, ed.), Cambridge University Press, Cambridge DOI: 10.1017/CCOL0521444608.005
46. Pakes, A., G. Gowrisankaran, and P. McGuire (1993), "Implementing the Pakes-McGuire algorithm for computing Markov perfect equilibria in Gauss." Working paper, Yale University, New Haven
47. Pakes, A. and P. McGuire (1994), "Computing Markov-perfect Nash equilibria: Numerical implications of a dynamic differentiated product model. Rand Journal of Economics, 25 (4), 555-589. DOI: 10.2307/2555975
48. Pakes, A. and P. McGuire (2001), "Stochastic algorithms, symmetric Markov perfect equilibrium, and the "curse" of dimensionality. Econometrica, 69 (5), 1261-1281. DOI: 10.1111/1468-0262.00241
49. Ryan, S. (2006), "The costs of environmental regulation in a concentrated industry." Working paper, MIT, Cambridge
50. Shapley, L. (1953), "Stochastic games. Proceedings of the National Academy of Sciences, 39, 1095-1100. DOI: 10.1073/pnas.39.10.1095
51. Simon, L. and M. Stinchcombe (1989), "Extensive form games in continuous time: Pure strategies. Econometrica, 57 (5), 1171-1214. DOI: 10.2307/1913627
52. Singer, B. and S. Spilerman (1976), "The representation of social processes by Markov models. American Journal of Sociology, 82 (1), 1-54. DOI: 10.1086/226269
53. Sobel, M. (1971), "Noncooperative stochastic games. Annals of Mathematical Statistics, 42 (6), 1930-1935. DOI: 10.1214/aoms/1177693059
54. Starr, A. and Y. Ho (1969), "Nonzero-sum differential games. Journal of Optimization Theory and Applications, 3 (3), 184-206. DOI: 10.1007/BF00929443
55. Whitt, W. (1980), "Representation and approximation of noncooperative sequential games. SIAM Journal of Control and Optimization, 18 (1), 33-48. DOI: 10.1137/0318003