IDEAS home Printed from https://ideas.repec.org/a/the/publsh/4624.html
   My bibliography  Save this article

Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk

Author

Listed:
  • Balbus, Lukasz

    (Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Gora)

  • Dziewulski, Pawel

    (Department of Economics, University of Sussex)

  • Reffett, Kevin

    (Department of Economics, Arizona State University)

  • Wozny, Lukasz

    (Department of Quantitative Economics, Warsaw School of Economics)

Abstract

We present a new approach to studying equilibrium dynamics in a class of stochastic games with a continuum of players with private types and strategic complementarities. We introduce a suitable equilibrium concept, called Markov Stationary Nash Distributional Equilibrium (MSNDE), prove its existence, and determine comparative statics of equilibrium paths and the steady state invariant distributions to which they converge. Finally, we provide numerous applications of our results including: dynamic models of growth with status concerns, social distance, and paternalistic bequests with endogenous preferences for consumption.

Suggested Citation

  • Balbus, Lukasz & Dziewulski, Pawel & Reffett, Kevin & Wozny, Lukasz, 2022. "Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk," Theoretical Economics, Econometric Society, vol. 17(2), May.
  • Handle: RePEc:the:publsh:4624
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20220725/33810/984
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Van Zandt, Timothy, 2010. "Interim Bayesian Nash equilibrium on universal type spaces for supermodular games," Journal of Economic Theory, Elsevier, vol. 145(1), pages 249-263, January.
    2. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
    3. Qiao, Lei & Yu, Haomiao & Zhang, Zhixiang, 2016. "On the closed-graph property of the Nash equilibrium correspondence in a large game: A complete characterization," Games and Economic Behavior, Elsevier, vol. 99(C), pages 89-98.
    4. Lawrence E. Blume & William A. Brock & Steven N. Durlauf & Rajshri Jayaraman, 2015. "Linear Social Interactions Models," Journal of Political Economy, University of Chicago Press, vol. 123(2), pages 444-496.
    5. Francesco Agostinelli & Matthias Doepke & Giuseppe Sorrenti & Fabrizio Zilibotti, 2020. "It Takes a Village: The Economics of Parenting with Neighborhood and Peer Effects," NBER Working Papers 27050, National Bureau of Economic Research, Inc.
    6. Łukasz Balbus & Paweł Dziewulski & Kevin Reffett & Łukasz Woźny, 2015. "Differential information in large games with strategic complementarities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 201-243, May.
    7. Kalai, Ehud & Shmaya, Eran, 2018. "Large strategic dynamic interactions," Journal of Economic Theory, Elsevier, vol. 178(C), pages 59-81.
    8. Echenique, Federico, 2004. "Extensive-form games and strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 348-364, February.
    9. 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.
    10. Matthias Doepke & Giuseppe Sorrenti & Fabrizio Zilibotti, 2019. "The Economics of Parenting," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 55-84, August.
    11. Angelo Mele, 2017. "A Structural Model of Dense Network Formation," Econometrica, Econometric Society, vol. 85, pages 825-850, May.
    12. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    13. Haiqing Xu, 2018. "Social Interactions In Large Networks: A Game Theoretic Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(1), pages 257-284, February.
    14. Adrien Auclert & Bence Bardóczy & Matthew Rognlie & Ludwig Straub, 2021. "Using the Sequence‐Space Jacobian to Solve and Estimate Heterogeneous‐Agent Models," Econometrica, Econometric Society, vol. 89(5), pages 2375-2408, September.
    15. Shuo Liu & Harry Pei, 2017. "Monotone equilibria in signalling games," ECON - Working Papers 252, Department of Economics - University of Zurich.
    16. Juan Carlos Parra-Alvarez & Olaf Posch & Mu-Chun Wang, 2017. "Estimation of Heterogeneous Agent Models: A Likelihood Approach," CESifo Working Paper Series 6717, CESifo.
    17. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
    18. George A. Akerlof, 1997. "Social Distance and Social Decisions," Econometrica, Econometric Society, vol. 65(5), pages 1005-1028, September.
    19. Ifrach, Bar & Weintraub, Gabriel Y., 2016. "A Framework for Dynamic Oligopoly in Concentrated Industries," Research Papers 3449, Stanford University, Graduate School of Business.
    20. George A. Akerlof & Rachel E. Kranton, 2000. "Economics and Identity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 115(3), pages 715-753.
    21. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 235-260.
    22. Mensch, Jeffrey, 2020. "On the existence of monotone pure-strategy perfect Bayesian equilibrium in games with complementarities," Journal of Economic Theory, Elsevier, vol. 187(C).
    23. Bergin, James & Bernhardt, Dan, 1992. "Anonymous sequential games with aggregate uncertainty," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 543-562.
    24. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2013. "Markov Stationary Equilibria in Stochastic Supermodular Games with Imperfect Private and Public Information," Dynamic Games and Applications, Springer, vol. 3(2), pages 187-206, June.
    25. Light, Bar & Weintraub, Gabriel, 2018. "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Research Papers 3731, Stanford University, Graduate School of Business.
    26. John K.‐H. Quah & Bruno Strulovici, 2012. "Aggregating the Single Crossing Property," Econometrica, Econometric Society, vol. 80(5), pages 2333-2348, September.
    27. Stephen Morris & Muhamet Yildiz, 2019. "Crises: Equilibrium Shifts and Large Shocks," American Economic Review, American Economic Association, vol. 109(8), pages 2823-2854, August.
    28. Matthias Doepke & Fabrizio Zilibotti, 2017. "Parenting With Style: Altruism and Paternalism in Intergenerational Preference Transmission," Econometrica, Econometric Society, vol. 85, pages 1331-1371, September.
    29. Federico Echenique, 2005. "A short and constructive proof of Tarski’s fixed-point theorem," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 215-218, June.
    30. Cole, Harold L & Mailath, George J & Postlewaite, Andrew, 1992. "Social Norms, Savings Behavior, and Growth," Journal of Political Economy, University of Chicago Press, vol. 100(6), pages 1092-1125, December.
    31. Daron Acemoglu & Matthew O. Jackson, 2017. "Social Norms and the Enforcement of Laws," Journal of the European Economic Association, European Economic Association, vol. 15(2), pages 245-295.
    32. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-877, October.
    33. Federico Echenique & Ivana Komunjer, 2009. "Testing Models With Multiple Equilibria by Quantile Methods," Econometrica, Econometric Society, vol. 77(4), pages 1281-1297, July.
    34. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    35. Konrad Podczeck, 2009. "On purification of measure-valued maps," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 399-418, February.
    36. He, Wei & Sun, Xiang & Sun, Yeneng, 2017. "Modeling infinitely many agents," Theoretical Economics, Econometric Society, vol. 12(2), May.
    37. Juan Carlos Parra-Alvarez & Olaf Posch & Mu-Chun Wang, 2017. "Identification and estimation of heterogeneous agent models: A likelihood approach," CREATES Research Papers 2017-35, Department of Economics and Business Economics, Aarhus University.
    38. Konrad Podczeck, 2010. "On existence of rich Fubini extensions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 1-22, October.
    39. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
    40. Alberto Bisin & Andrea Moro & Giorgio Topa, 2011. "The empirical content of models with multiple equilibria in economies with social interactions," Staff Reports 504, Federal Reserve Bank of New York.
    41. Huggett, Mark, 1997. "The one-sector growth model with idiosyncratic shocks: Steady states and dynamics," Journal of Monetary Economics, Elsevier, vol. 39(3), pages 385-403, August.
    42. Angeletos, George-Marios & Calvet, Laurent-Emmanuel, 2005. "Incomplete-market dynamics in a neoclassical production economy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 407-438, August.
    43. Garance Genicot & Debraj Ray, 2017. "Aspirations and Inequality," Econometrica, Econometric Society, vol. 85, pages 489-519, March.
    44. Rabah Amir, 2002. "Complementarity and Diagonal Dominance in Discounted Stochastic Games," Annals of Operations Research, Springer, vol. 114(1), pages 39-56, August.
    45. Ennio Bilancini & Leonardo Boncinelli, 2016. "Strict Nash equilibria in non-atomic games with strict single crossing in players (or types) and actions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 95-109, April.
    46. Rene Carmona & Francois Delarue & Daniel Lacker, 2016. "Mean field games of timing and models for bank runs," Papers 1606.03709, arXiv.org, revised Jan 2017.
    47. Qiao, Lei & Yu, Haomiao, 2014. "On the space of players in idealized limit games," Journal of Economic Theory, Elsevier, vol. 153(C), pages 177-190.
    48. J. B. Taylor & Harald Uhlig (ed.), 2016. "Handbook of Macroeconomics," Handbook of Macroeconomics, Elsevier, edition 1, volume 2, number 2.
    49. Ioannis Karatzas & Martin Shubik & William D. Sudderth, 1994. "Construction of Stationary Markov Equilibria in a Strategic Market Game," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 975-1006, November.
    50. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    51. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
    52. George-Marios Angeletos & Chen Lian, 2016. "Incomplete Information in Macroeconomics: Accommodating Frictions in Coordination," NBER Working Papers 22297, National Bureau of Economic Research, Inc.
    53. Angeletos, G.-M. & Lian, C., 2016. "Incomplete Information in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 1065-1240, Elsevier.
    54. Cao, Dan, 2020. "Recursive equilibrium in Krusell and Smith (1998)," Journal of Economic Theory, Elsevier, vol. 186(C).
    55. Adlakha, Sachin & Johari, Ramesh & Weintraub, Gabriel Y., 2015. "Equilibria of dynamic games with many players: Existence, approximation, and market structure," Journal of Economic Theory, Elsevier, vol. 156(C), pages 269-316.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Uttiya Paul & Tarun Sabarwal, 2023. "Directional monotone comparative statics in function spaces," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 153-169, April.
    2. Aniruddha Ghosh, 2024. "Robust Comparative Statics with Misspecified Bayesian Learning," Papers 2407.17037, arXiv.org.
    3. Tarun Sabarwal, 2023. "Universal Theory of Equilibrium in Models with Complementarities," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202312, University of Kansas, Department of Economics, revised Nov 2023.
    4. Tarun Sabarwal, 2023. "General theory of equilibrium in models with complementarities," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202307, University of Kansas, Department of Economics, revised Sep 2023.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Datta, Manjira & Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2005. "Markovian equilibrium in infinite horizon economies with incomplete markets and public policy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 505-544, August.
    2. Jian Yang, 2021. "Analysis of Markovian Competitive Situations Using Nonatomic Games," Dynamic Games and Applications, Springer, vol. 11(1), pages 184-216, March.
    3. Łukasz Balbus & Paweł Dziewulski & Kevin Reffett & Łukasz Woźny, 2019. "A qualitative theory of large games with strategic complementarities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 497-523, April.
    4. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
    5. Khieu, Hoang & Wälde, Klaus, 2023. "Capital income risk and the dynamics of the wealth distribution," Economic Modelling, Elsevier, vol. 122(C).
    6. Wu, Bin, 2022. "On pure-strategy Nash equilibria in large games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 305-315.
    7. Khan, Mohammed Ali & Rath, Kali P. & Yu, Haomiao & Zhang, Yongchao, 2017. "On the equivalence of large individualized and distributionalized games," Theoretical Economics, Econometric Society, vol. 12(2), May.
    8. Cao, Dan, 2020. "Recursive equilibrium in Krusell and Smith (1998)," Journal of Economic Theory, Elsevier, vol. 186(C).
    9. ÖZGÜR, Onur & BISIN, Alberto, 2011. "Dynamic Linear Economies with Social Interactions," Cahiers de recherche 04-2011, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    10. Miao, Jianjun, 2006. "Competitive equilibria of economies with a continuum of consumers and aggregate shocks," Journal of Economic Theory, Elsevier, vol. 128(1), pages 274-298, May.
    11. Fu, Haifeng & Wu, Bin, 2019. "Characterization of Nash equilibria of large games," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 46-51.
    12. Chen, Enxian & Qiao, Lei & Sun, Xiang & Sun, Yeneng, 2022. "Robust perfect equilibrium in large games," Journal of Economic Theory, Elsevier, vol. 201(C).
    13. Łukasz Balbus & Paweł Dziewulski & Kevin Reffett & Łukasz Woźny, 2015. "Differential information in large games with strategic complementarities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 201-243, May.
    14. Kanbur, Ravi & Fleurbaey, Marc, 2021. "Efficiency and equity in a society-economy integrated model," CEPR Discussion Papers 16446, C.E.P.R. Discussion Papers.
    15. Li, Fei & Song, Yangbo & Zhao, Mofei, 2023. "Global manipulation by local obfuscation," Journal of Economic Theory, Elsevier, vol. 207(C).
    16. Kojevnikov, Denis & Song, Kyungchul, 2023. "Econometric inference on a large Bayesian game with heterogeneous beliefs," Journal of Econometrics, Elsevier, vol. 237(1).
    17. Brenøe, Anne Ardila & Epper, Thomas, 2022. "Parenting values and the intergenerational transmission of time preferences," European Economic Review, Elsevier, vol. 148(C).
    18. Timur Kuran & William H. Sandholm, 2008. "Cultural Integration and Its Discontents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(1), pages 201-228.
    19. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng & Yu, Haomiao, 2013. "Large games with a bio-social typology," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1122-1149.
    20. Grajzl, Peter & Baniak, Andrzej, 2012. "Mandating behavioral conformity in social groups with conformist members," Journal of Economic Behavior & Organization, Elsevier, vol. 82(2), pages 479-493.

    More about this item

    Keywords

    Large games; distributional equilibria; supermodular games; comparative dynamics; non-aggregative games; social interactions;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:the:publsh:4624. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Martin J. Osborne (email available below). General contact details of provider: http://econtheory.org .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.