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Protocol invariance and the timing of decisions in dynamic games

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  • Doraszelski, Ulrich

    (Wharton School, University of Pennsylvania)

  • Escobar, Juan F.

    (Department of Industrial Engineering, University of Chile)

Abstract

We characterize a class of dynamic stochastic games that we call separable dynamic games with noisy transitions and establish that these widely used models are protocol invariant provided that periods are sufficiently short. Protocol invariance means that the set of Markov perfect equilibria is nearly the same irrespective of the order in which players are assumed to move within a period. Protocol invariance can facilitate applied work and renders the implications and predictions of a model more robust. Our class of dynamic stochastic games includes investment games, R\&D races, models of industry dynamics, dynamic public contribution games, asynchronously repeated games, and many other models from the extant literature.

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  • Doraszelski, Ulrich & Escobar, Juan F., 2019. "Protocol invariance and the timing of decisions in dynamic games," Theoretical Economics, Econometric Society, vol. 14(2), May.
    • Handle: RePEc:the:publsh:3230
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    1. Bhaskar, V. & Vega-Redondo, Fernando, 2002. "Asynchronous Choice and Markov Equilibria," Journal of Economic Theory, Elsevier, vol. 103(2), pages 334-350, April.
    2. Maskin, Eric & Tirole, Jean, 1987. "A theory of dynamic oligopoly, III : Cournot competition," European Economic Review, Elsevier, vol. 31(4), pages 947-968, June.
    3. 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.
    4. Leslie M. Marx & Steven A. Matthews, 2000. "Dynamic Voluntary Contribution to a Public Project," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(2), pages 327-358.
    5. A. Michael Spence, 1979. "Investment Strategy and Growth in a New Market," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 1-19, Spring.
    6. 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.
    7. Richard F. Serfozo, 1979. "Technical Note—An Equivalence Between Continuous and Discrete Time Markov Decision Processes," Operations Research, INFORMS, vol. 27(3), pages 616-620, June.
    8. Yuliy Sannikov & Andrzej Skrzypacz, 2007. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," American Economic Review, American Economic Association, vol. 97(5), pages 1794-1823, December.
    9. Doraszelski, Ulrich & Pakes, Ariel, 2007. "A Framework for Applied Dynamic Analysis in IO," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 30, pages 1887-1966, Elsevier.
    10. Drew Fudenberg & David Levine, 2008. "Limit Games and Limit Equilibria," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 2, pages 21-39, World Scientific Publishing Co. Pte. Ltd..
    11. van Damme, Eric & Hurkens, Sjaak, 1996. "Commitment Robust Equilibria and Endogenous Timing," Games and Economic Behavior, Elsevier, vol. 15(2), pages 290-311, August.
    12. Gabriel Y. Weintraub & C. Lanier Benkard & Benjamin Van Roy, 2008. "Markov Perfect Industry Dynamics With Many Firms," Econometrica, Econometric Society, vol. 76(6), pages 1375-1411, November.
    13. , & ,, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
    14. Paul Ellickson & Patrick Bayer & Jason Blevins & Peter Arcidiacono, 2010. "Estimation of Dynamic Discrete Choice Models in Continuous Time," 2010 Meeting Papers 70, Society for Economic Dynamics.
    15. Ulrich Doraszelski & Kenneth L. Judd, 2012. "Avoiding the curse of dimensionality in dynamic stochastic games," Quantitative Economics, Econometric Society, vol. 3(1), pages 53-93, March.
    16. 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.
    17. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
    18. J. Aislinn Bohren, 2011. "Stochastic Games in Continuous Time: Persistent Actions in Long-Run Relationships, Second Version," PIER Working Paper Archive 14-033, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Aug 2014.
    19. Roger Lagunoff & Akihiko Matsui, 1997. "Asynchronous Choice in Repeated Coordination Games," Econometrica, Econometric Society, vol. 65(6), pages 1467-1478, November.
    20. Simon, Leo K. & Stinchcombe, Maxwell B., 1987. "Extensive From Games in Continuous Time: Pure Strategies," Department of Economics, Working Paper Series qt03x115sh, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    21. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
    22. Ulrich Doraszelski & Sarit Markovich, 2007. "Advertising dynamics and competitive advantage," RAND Journal of Economics, RAND Corporation, vol. 38(3), pages 557-592, September.
    23. Reynolds, Stanley S., 1991. "Dynamic oligopoly with capacity adjustment costs," Journal of Economic Dynamics and Control, Elsevier, vol. 15(3), pages 491-514, July.
    24. Guillermo Caruana & Liran Einav, 2008. "A Theory of Endogenous Commitment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(1), pages 99-116.
    25. George Georgiadis, 2015. "Projects and Team Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(1), pages 187-218.
    26. Bergemann, Dirk & Valimaki, Juuso, 1996. "Learning and Strategic Pricing," Econometrica, Econometric Society, vol. 64(5), pages 1125-1149, September.
    27. Reinganum, Jennifer F, 1982. "A Dynamic Game of R and D: Patent Protection and Competitive Behavior," Econometrica, Econometric Society, vol. 50(3), pages 671-688, May.
    28. Fudenberg, Drew & Tirole, Jean, 1983. "Capital as a commitment: Strategic investment to deter mobility," Journal of Economic Theory, Elsevier, vol. 31(2), pages 227-250, December.
    29. V. Bhaskar & George J. Mailathy & Stephen Morris, 2009. "A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games," Levine's Working Paper Archive 814577000000000178, David K. Levine.
    30. Peter Arcidiacono & Patrick Bayer & Jason R. Blevins & Paul B. Ellickson, 2016. "Estimation of Dynamic Discrete Choice Models in Continuous Time with an Application to Retail Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(3), pages 889-931.
    31. de Roos, Nicolas, 2004. "A model of collusion timing," International Journal of Industrial Organization, Elsevier, vol. 22(3), pages 351-387, March.
    32. Fedor Iskhakov & John Rust & Bertel Schjerning, 2016. "Recursive Lexicographical Search: Finding All Markov Perfect Equilibria of Finite State Directional Dynamic Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(2), pages 658-703.
    33. Berry, Steven T, 1992. "Estimation of a Model of Entry in the Airline Industry," Econometrica, Econometric Society, vol. 60(4), pages 889-917, July.
    34. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    35. Giovannetti, Emanuele, 2001. "Perpetual Leapfrogging in Bertrand Duopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 671-696, August.
    36. Michael D. Noel, 2008. "Edgeworth Price Cycles and Focal Prices: Computational Dynamic Markov Equilibria," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 17(2), pages 345-377, June.
    37. Christopher Harris & John Vickers, 1987. "Racing with Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 1-21.
    38. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 53-82.
    39. Rubinstein Ariel & Wolinsky Asher, 1995. "Remarks on Infinitely Repeated Extensive-Form Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 110-115, April.
    40. Liran Einav, 2010. "Not All Rivals Look Alike: Estimating An Equilibrium Model Of The Release Date Timing Game," Economic Inquiry, Western Economic Association International, vol. 48(2), pages 369-390, April.
    41. Chen, Jiawei, 2009. "The effects of mergers with dynamic capacity accumulation," International Journal of Industrial Organization, Elsevier, vol. 27(1), pages 92-109, January.
    42. Berry, Steven & Pakes, Ariel, 1993. "Some Applications and Limitations of Recent Advances in Empirical Industrial Organization: Merger Analysis," American Economic Review, American Economic Association, vol. 83(2), pages 247-252, May.
    43. Bar Ifrach & Gabriel Y. Weintraub, 2017. "A Framework for Dynamic Oligopoly in Concentrated Industries," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(3), pages 1106-1150.
    44. Yoon, Kiho, 2001. "A Folk Theorem for Asynchronously Repeated Games," Econometrica, Econometric Society, vol. 69(1), pages 191-200, January.
    45. , & ,, 2015. "A folk theorem for stochastic games with infrequent state changes," Theoretical Economics, Econometric Society, vol. 10(1), January.
    46. Markovich, Sarit, 2008. "Snowball: A dynamic oligopoly model with indirect network effects," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 909-938, March.
    47. Cahuc, Pierre & Kempf, Hubert, 1997. "Alternative Time Patterns of Decisions and Dynamic Strategic Interactions," Economic Journal, Royal Economic Society, vol. 107(445), pages 1728-1741, November.
    48. Hans Haller & Roger Lagunoff, 2000. "Genericity and Markovian Behavior in Stochastic Games," Econometrica, Econometric Society, vol. 68(5), pages 1231-1248, September.
    49. Dockner, Engelbert J, 1992. "A Dynamic Theory of Conjectural Variations," Journal of Industrial Economics, Wiley Blackwell, vol. 40(4), pages 377-395, December.
    50. Dilip Abreu & Faruk Gul, 2000. "Bargaining and Reputation," Econometrica, Econometric Society, vol. 68(1), pages 85-118, January.
    51. Michael J. Mazzeo, 2002. "Product Choice and Oligopoly Market Structure," RAND Journal of Economics, The RAND Corporation, vol. 33(2), pages 221-242, Summer.
    52. Attila Ambrus & Yuhta Ishii, 2015. "On Asynchronicity of Moves and Coordination," Levine's Bibliography 786969000000001146, UCLA Department of Economics.
    53. Kathleen Cleeren & Frank Verboven & Marnik G. Dekimpe & Katrijn Gielens, 2010. "Intra- and Interformat Competition Among Discounters and Supermarkets," Marketing Science, INFORMS, vol. 29(3), pages 456-473, 05-06.
    54. Quan Wen, 2002. "A Folk Theorem for Repeated Sequential Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(2), pages 493-512.
    55. Riordan, Michael H & Salant, David J, 1994. "Preemptive Adoptions of an Emerging Technology," Journal of Industrial Economics, Wiley Blackwell, vol. 42(3), pages 247-261, September.
    56. HALKIN, Hubert, 1974. "Implicit functions and optimization problems without continuous differentiability of the data," LIDAM Reprints CORE 184, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    57. Grossman, Gene M & Shapiro, Carl, 1987. "Dynamic R&D Competition," Economic Journal, Royal Economic Society, vol. 97(386), pages 372-387, June.
    58. Simon, Leo K & Stinchcombe, Maxwell B, 1989. "Extensive Form Games in Continuous Time: Pure Strategies," Econometrica, Econometric Society, vol. 57(5), pages 1171-1214, September.
    59. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
    60. Fudenberg, Drew & Gilbert, Richard & Stiglitz, Joseph & Tirole, Jean, 1983. "Preemption, leapfrogging and competition in patent races," European Economic Review, Elsevier, vol. 22(1), pages 3-31, June.
    61. Steve A. Lippman & Kevin F. McCardle, 1987. "Dropout Behavior in R&D Races with Learning," RAND Journal of Economics, The RAND Corporation, vol. 18(2), pages 287-295, Summer.
    62. Fedor Iskhakov & John Rust & Bertel Schjerning, 2018. "The Dynamics Of Bertrand Price Competition With Cost‐Reducing Investments," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(4), pages 1681-1731, November.
    63. Johannes Hörner & Takuo Sugaya & Satoru Takahashi & Nicolas Vieille, 2011. "Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→ 1 and a Folk Theorem," Econometrica, Econometric Society, vol. 79(4), pages 1277-1318, July.
    64. Reynolds, Stanley S, 1987. "Capacity Investment, Preemption and Commitment in an Infinite Horizon Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 69-88, February.
    65. Olivier Compte & Philippe Jehiel, 2004. "Gradualism in Bargaining and Contribution Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(4), pages 975-1000.
    66. Bernheim, B. Douglas & Ray, Debraj, 1989. "Markov perfect equilibria in altruistic growth economies with production uncertainty," Journal of Economic Theory, Elsevier, vol. 47(1), pages 195-202, February.
    67. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    68. , & , & , & ,, 2014. "Asynchronicity and coordination in common and opposing interest games," Theoretical Economics, Econometric Society, vol. 9(2), May.
    69. Raghavan, T.E.S. & Tijs, S.H. & Vrieze, O.J., 1985. "On stochastic games with additive reward and transition structure," Other publications TiSEM 28f85a14-9a6e-4ed8-9a4b-a, Tilburg University, School of Economics and Management.
    70. McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142, Elsevier.
    71. R. M. Cyert & M. H. DeGroot, 1970. "Multiperiod Decision Models with Alternating Choice as a Solution to the Duopoly Problem," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 84(3), pages 410-429.
    72. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
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    More about this item

    Keywords

    Dynamic stochastic games; timing of decisions; commitment; protocol invariance;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D0 - Microeconomics - - General

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