Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics

Published Online:https://doi.org/10.1287/opre.2020.2090

References

  • Acemoglu D, Jensen MK (2015) Robust comparative statics in large dynamic economies. J. Political Econom. 123(3):587–640.CrossrefGoogle Scholar
  • Acemoglu D, Jensen MK (2018) Equilibrium analysis in the behavioral neoclassical growth model. Working paper, Massachusetts Institute of Technology, Cambridge.Google Scholar
  • Acikgoz O (2018) On the existence and uniqueness of stationary equilibrium in Bewley economies with production. J. Econom. Theory 173(C):18–55.CrossrefGoogle Scholar
  • Adlakha S, Johari R (2013) Mean field equilibrium in dynamic games with strategic complementarities. Oper. Res. 61(4):971–989.LinkGoogle Scholar
  • Adlakha S, Johari R, Weintraub GY (2015) Equilibria of dynamic games with many players: Existence, approximation, and market structure. J. Econom. Theory 156:269–316.CrossrefGoogle Scholar
  • Aiyagari SR (1994) Uninsured idiosyncratic risk and aggregate saving. Quart. J. Econom. 109(3):659–684.CrossrefGoogle Scholar
  • Aliprantis CD, Border K (2006) Infinite Dimensional Analysis: A Hitchhiker’s Guide (Springer, New York).Google Scholar
  • Aperjis C, Johari R (2010) Optimal windows for aggregating ratings in electronic marketplaces. Management Sci. 56(5):864–880.LinkGoogle Scholar
  • Arnosti N, Johari R, Kanoria Y (2022) Managing congestion in matching markets. Manufacturing Service Oper. Management. Forthcoming.Google Scholar
  • Balseiro SR, Besbes O, Weintraub GY (2015) Repeated auctions with budgets in ad exchanges: Approximations and design. Management Sci. 61(4):864–884.LinkGoogle Scholar
  • Bertsekas DP, Shreve SE (1978) Stochastic Optimal Control: The Discrete Time Case (Academic Press, New York).Google Scholar
  • Bertsekas D, Nedi A, Ozdaglar A (2003) Convex Analysis and Optimization (Athena Scientific).Google Scholar
  • Besanko D, Doraszelski U (2004) Capacity dynamics and endogenous asymmetries in firm size. RAND J. Econom. 35(1):23–49.CrossrefGoogle Scholar
  • Besanko D, Perry MK, Spady RH (1990) The logit model of monopolistic competition: Brand diversity. J. Indust. Econom. 38(4):397–415.CrossrefGoogle Scholar
  • Besanko D, Doraszelski U, Lu LX, Satterthwaite M (2010) Lumpy capacity investment and disinvestment dynamics. Oper. Res. 58(4):1178–1193.Google Scholar
  • Besbes O, Scarsini M (2018) On information distortions in online ratings. Oper. Res. 66(3):597–610.LinkGoogle Scholar
  • Bewley T (1986) Stationary monetary equilibrium with a continuum of independently fluctuating consumers. Hildenbrand W, Mas-Colell A, eds. Contributions to Mathematical Economics in Honor of Gérard Debreu (North-Holland), 79–102.Google Scholar
  • Bhattacharya RN, Lee O (1988) Asymptotics of a class of Markov processes which are not in general irreducible. Ann. Probab. 16(3):1333–1347.CrossrefGoogle Scholar
  • Bimpikis K, Elmaghraby WJ, Moon K, Zhang W (2020) Managing market thickness in online b2b markets. Management Sci. 66(12):5783–5822.LinkGoogle Scholar
  • Bolton G, Greiner B, Ockenfels A (2013) Engineering trust: Reciprocity in the production of reputation information. Management Sci. 59(2):265–285.LinkGoogle Scholar
  • Caplin A, Nalebuff B (1991) Aggregation and imperfect competition: On the existence of equilibrium. Econometrica 59(1):25–59.CrossrefGoogle Scholar
  • Carmona R, Delarue F (2018) Probabilistic Theory of Mean Field Games with Applications I-II (Springer).CrossrefGoogle Scholar
  • Dellarocas C (2003) The digitization of word of mouth: Promise and challenges of online feedback mechanisms. Management Sci. 49(10):1407–1424.LinkGoogle Scholar
  • Doraszelski U, Pakes A (2007) A framework for applied dynamic analysis in IO. Armstrong M, Porter R, eds. The Handbook of Industrial Organization, vol. 3 (Elsevier, New York), 2183–2162.Google Scholar
  • Doraszelski U, Satterthwaite M (2010) Computable Markov-perfect industry dynamics. RAND J. Econom. 41(2):215–243.CrossrefGoogle Scholar
  • Ericson R, Pakes A (1995) Markov-perfect industry dynamics: A framework for empirical work. Rev. Econom. Stud. 62(1):53–82.CrossrefGoogle Scholar
  • Friesz TL, Bernstein D, Smith TE, Tobin RL, Wie BW (1993) A variational inequality formulation of the dynamic network user equilibrium problem. Oper. Res. 41(1):179–191.LinkGoogle Scholar
  • Hall J, Porteus E (2000) Customer service competition in capacitated systems. Manufacturing Service Oper. Management 2(2):144–165.LinkGoogle Scholar
  • He W, Sun Y (2017) Stationary Markov perfect equilibria in discounted stochastic games. J. Econom. Theory 169:35–61.CrossrefGoogle Scholar
  • Heathcote J, Storesletten K, Violante GL (2009) Quantitative macroeconomics with heterogeneous households. Annual. Rev. Econom. 1:319–352.CrossrefGoogle Scholar
  • Heyman DP, Sobel MJ (2004) Stochastic Models in Operations Research: Stochastic Optimization, vol. 2 (Courier Corporation).Google Scholar
  • Hopenhayn HA (1992) Entry, exit, and firm dynamics in long run equilibrium. Econometrica 60(5):1127–1150.CrossrefGoogle Scholar
  • Hopenhayn HA, Prescott EC (1992) Stochastic monotonicity and stationary distributions for dynamic economies. Econometrica 60(6):1387–1406.CrossrefGoogle Scholar
  • Hu TW, Shmaya E (2019) Unique monetary equilibrium with inflation in a stationary Bewley–Aiyagari model. J. Econom. Theory 180:368–382.CrossrefGoogle Scholar
  • Huang M, Malhamé RP, Caines PE (2006) Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Comm. Inform. Systems 6(3):221–252.CrossrefGoogle Scholar
  • Ifrach B, Weintraub GY (2016) A framework for dynamic oligopoly in concentrated industries. Rev. Econom. Stud. 84(3):1106–1150.Google Scholar
  • Iyer K, Johari R, Sundararajan M (2014) Mean field equilibria of dynamic auctions with learning. Management Sci. 60(12):2949–2970.LinkGoogle Scholar
  • Jovanovic B, Rosenthal RW (1988) Anonymous sequential games. J. Math. Econom. 17(1):77–87.CrossrefGoogle Scholar
  • Kamae T, Krengel U, O’Brien GL (1977) Stochastic inequalities on partially ordered spaces. Ann. Probab. 5(6):899–912.CrossrefGoogle Scholar
  • Kanoria Y, Saban D (2022) Facilitating the search for partners on matching platforms. Working paper, Management Sci. Forthcoming.Google Scholar
  • Lasry JM, Lions PL (2007) Mean field games. Japanese J. Math. 2:229–260.CrossrefGoogle Scholar
  • Light B (2020) Uniqueness of equilibrium in a BEWLEY-AIYagari model. Econom. Theory 69:435–450.CrossrefGoogle Scholar
  • Maskin E, Tirole J (2001) Markov perfect equilibrium I. Observable actions. J. Econom. Theory 100(2):191–219.CrossrefGoogle Scholar
  • Meyn SP, Tweedie RL (2012) Markov Chains and Stochastic Stability (Springer Science & Business Media, New York).Google Scholar
  • Milgrom P, Roberts J (1994) Comparing equilibria. Amer. Econom. Rev. 84(3):441–459.Google Scholar
  • Olsen TL, Parker RP (2014) On Markov equilibria in dynamic inventory competition. Oper. Res. 62(2):332–344.LinkGoogle Scholar
  • Onishi K (2016) Quantity discounts and capital misallocation in vertical relationships: The case of aircraft and airline industries. Working paper, Singapore Management University, Singapore.Google Scholar
  • Pakes A, McGuire P (1994) Computing Markov-perfect Nash equilibria: Numerical implications of a dynamic differentiated product model. RAND J. Econom. 25(4):555–589.CrossrefGoogle Scholar
  • Papanastasiou Y, Bimpikis K, Savva N (2017) Crowdsourcing exploration. Management Sci. 64(4):1727–1746.LinkGoogle Scholar
  • Qi S (2013) The impact of advertising regulation on industry: The cigarette advertising ban of 1971. RAND J. Econom. 44(2):215–248.CrossrefGoogle Scholar
  • Serfozo R (1982) Convergence of Lebesgue integrals with varying measures. Sankhya Ser. A. 44(3):380–402.Google Scholar
  • Shapley LS (1953) Stochastic games. Proc. Natl. Acad. Sci. 39(10):1095–1100.Google Scholar
  • Stokey N, Lucas R (1989) Recursive Methods in Economic Dynamics (Harvard University Press).CrossrefGoogle Scholar
  • Tadelis S (2016) Reputation and feedback systems in online platform markets. Annual Rev. Econom. 8:321–340.CrossrefGoogle Scholar
  • Tembine H, Le Boudec JY, El-Azouzi R, Altman E (2009) Mean field asymptotics of Markov decision evolutionary games and teams. (Univ Illiniois at Urbana-Champaign, Istanbul). Başar T, ed. Internat. Conf. Game Theory Networks (IEEE) (Univ Illiniois at Urbana-Champaign, Istanbul), 140–150.Google Scholar
  • Topkis DM (1979) Equilibrium points in nonzero-sum n-person submodular games. SIAM J. Control Optim. 17(6):773–787.CrossrefGoogle Scholar
  • Topkis DM (2011) Supermodularity and Complementarity (Princeton University Press).CrossrefGoogle Scholar
  • Weintraub GY, Benkard CL, Van Roy B (2008) Markov perfect industry dynamics with many firms. Econometrica 76(6):1375–1411.CrossrefGoogle Scholar
  • Xu J, Hajek B (2013) The supermarket game. Stochastic Systems 3(2):405–441.LinkGoogle Scholar
  • Yang P, Iyer K, Frazier P (2018) Mean field equilibria for resource competition in spatial settings. Stochastic Systems 8(4):307–334.LinkGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.