1932

Abstract

This review focuses on properties related to the robustness and stability of Nash equilibria in games with a large number of players. Somewhat surprisingly, these equilibria become substantially more robust and stable as the number of players increases. We illustrate the relevant phenomena through a binary-action game with strategic substitutes, framed as a game of social isolation in a pandemic environment.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-economics-072720-042303
2021-08-05
2024-06-17
Loading full text...

Full text loading...

/deliver/fulltext/economics/13/1/annurev-economics-072720-042303.html?itemId=/content/journals/10.1146/annurev-economics-072720-042303&mimeType=html&fmt=ahah

Literature Cited

  1. Abraham I, Dolev D, Gonen R, Halpern J. 2006. Distributed computing meets game theory: robust mechanisms for rational secret sharing and multiparty computation. Proceedings of the Twenty-Fifth Annual ACM Symposium on Principles of Distributed Computing53–62 New York: ACM
    [Google Scholar]
  2. Acemoglu D, Chernozhukov V, Werning I, Whinston MD. 2020. Optimal targeted lockdowns in a multi-group SIR model NBER Work. Pap. 27102
    [Google Scholar]
  3. Acemoglu D, Jensen MK. 2013. Aggregate comparative statics. Games Econ. Behav. 81:27–49
    [Google Scholar]
  4. Adda J. 2016. Economic activity and the spread of viral diseases: evidence from high frequency data. Q. J. Econ. 131:891–941
    [Google Scholar]
  5. Al-Najjar NI. 2008. Large games and the law of large numbers. Games Econ. Behav. 64:1–34
    [Google Scholar]
  6. Al-Najjar NI, Smorodinsky R 2001. Large nonanonymous repeated games. Games Econ. Behav. 37:26–39
    [Google Scholar]
  7. Alon N, Spencer JH. 2004. The Probabilistic Method Hoboken, NJ: Wiley
    [Google Scholar]
  8. Alvarez FE, Argente D, Lippi F. 2020. A simple planning problem for COVID-19 lockdown NBER Work. Pap. 26981
    [Google Scholar]
  9. Aumann RJ, Shapley LS. 1974. Values of Non-Atomic Games Princeton, NJ: Princeton Univ. Press
    [Google Scholar]
  10. Azevedo EM, Budish E. 2019. Strategy-proofness in the large. Rev. Econ. Stud. 86:81–116
    [Google Scholar]
  11. Azrieli Y, Shmaya E. 2013. Lipschitz games. Math. Oper. Res. 38:350–57
    [Google Scholar]
  12. Babichenko Y, Barman S, Peretz R. 2014. Simple approximate equilibria in large games. Proceedings of the Fifteenth ACM Conference on Economics and Computation753–70 New York: ACM
    [Google Scholar]
  13. Blonski M. 1999. Anonymous games with binary actions. Games Econ. Behav. 28:171–80
    [Google Scholar]
  14. Bodoh-Creed A. 2013. Efficiency and information aggregation in large uniform-price auctions. J. Econ. Theory 148:2436–66
    [Google Scholar]
  15. Carmona G. 2008. Purification of Bayesian–Nash equilibria in large games with compact type and action spaces. J. Math. Econ. 44:1302–11
    [Google Scholar]
  16. Carmona G, Podczeck K. 2012. Ex-post stability of Bayes–Nash equilibria of large games. Games Econ. Behav. 74:418–30
    [Google Scholar]
  17. Carmona G, Podczeck K. 2020. Strict pure strategy Nash equilibria in large finite-player games. Theor. Econ In press
    [Google Scholar]
  18. Carroll G. 2019. Robustness in mechanism design and contracting. Annu. Rev. Econ. 11:139–66
    [Google Scholar]
  19. Cartwright E, Wooders M. 2009. On equilibrium in pure strategies in games with many players. Int. J. Game Theory 38:137–53
    [Google Scholar]
  20. Cerreia-Vioglio S, Maccheroni F, Schmeidler D. 2020. Equilibria of nonatomic anonymous games. arXiv:2005.01839 [econ.TH]
  21. Che YK, Tercieux O. 2019. Efficiency and stability in large matching markets. J. Political Econ. 127:2301–42
    [Google Scholar]
  22. Cole R, Tao Y. 2016. Large market games with near optimal efficiency. Proceedings of the 2016 ACM Conference on Economics and Computation791–808 New York: ACM
    [Google Scholar]
  23. Daskalakis C, Papadimitriou CH. 2015. Approximate Nash equilibria in anonymous games. J. Econ. Theory 156:207–45
    [Google Scholar]
  24. Deb J, Kalai E. 2015. Stability in large Bayesian games with heterogeneous players. J. Econ. Theory 157:1041–55
    [Google Scholar]
  25. Eliaz K. 2002. Fault tolerant implementation. Rev. Econ. Stud. 69:589–610
    [Google Scholar]
  26. Farboodi M, Jarosch G, Shimer R. 2020. Internal and external effects of social distancing in a pandemic NBER Work. Pap. 27059
    [Google Scholar]
  27. Gaffeo E. 2003. The economics of HIV/AIDS: a survey. Dev. Policy Rev. 21:27–49
    [Google Scholar]
  28. Galeotti A, Goyal S, Jackson MO, Vega-Redondo F, Yariv L 2010. Network games. Rev. Econ. Stud. 77:218–44
    [Google Scholar]
  29. Geoffard PY, Philipson T. 1996. Rational epidemics and their public control. Int. Econ. Rev. 37:603–24
    [Google Scholar]
  30. Goenka A, Liu L. 2012. Infectious diseases and endogenous fluctuations. Econ. Theory 50:125–49
    [Google Scholar]
  31. Gradwohl R, Reingold O. 2007. Partial exposure and correlated types in large games Work. Pap., Weizmann Inst. Sci. Rehovot, Isr:.
    [Google Scholar]
  32. Gradwohl R, Reingold O. 2010. Partial exposure in large games. Games Econ. Behav. 68:602–13
    [Google Scholar]
  33. Gradwohl R, Reingold O. 2014. Fault tolerance in large games. Games Econ. Behav. 86:438–57
    [Google Scholar]
  34. Gradwohl R, Yehudayoff A. 2008. t-Wise independence with local dependencies. Inf. Process. Lett. 106:208–12
    [Google Scholar]
  35. Green EJ. 1982. Noncooperative price taking in large dynamic markets. Noncooperative Approaches to the Theory of Perfect Competition, ed. A Mas-Colell 37–64 New York: Academic
    [Google Scholar]
  36. Greenwood J, Kircher P, Santos C, Tertilt M. 2019. An equilibrium model of the African HIV/AIDS epidemic. Econometrica 87:1081–113
    [Google Scholar]
  37. Jensen MK. 2010. Aggregative games and best-reply potentials. Econ. Theory 43:45–66
    [Google Scholar]
  38. Jordan JS, Radner R. 1982. Rational expectations in microeconomic models: an overview. J. Econ. Theory 26:201–23
    [Google Scholar]
  39. Kalai E. 2004. Large robust games. Econometrica 72:1631–65
    [Google Scholar]
  40. Kalai E 2008. Large games: structural robustness. The New Palgrave Dictionary of Economics S Durlauf, LE Blume 920–32 Basingstoke, UK: Palgrave Macmillan. , 2nd ed..
    [Google Scholar]
  41. Kalai E. 2018. Viable Nash equilibria: formation and defection. Work. Pap., Northwest. Univ Evanston, IL:
    [Google Scholar]
  42. Kalai E, Shmaya E. 2017. Learning, predictions, and stability in large dynamic interactions. Work. Pap., Northwest. Univ. Evanston, IL:
    [Google Scholar]
  43. Kalai E, Shmaya E. 2018. Large strategic dynamic interactions. J. Econ. Theory 178:59–81
    [Google Scholar]
  44. Kearns M, Pai M, Roth A, Ullman J 2014. Mechanism design in large games: incentives and privacy. Proceedings of the 5th Conference on Innovations in Theoretical Computer Science403–10 New York: ACM
    [Google Scholar]
  45. Keppo J, Quercioli E, Kudlyak M, Wilson A, Smith L 2020. The behavioral SIR model, with applications to the swine flu and COVID-19 pandemics Virtual Macro Pres Apr. 10. https://www.lonessmith.com/wp-content/uploads/2020/04/pandemic-slides.pdf
    [Google Scholar]
  46. Kermack WO, McKendrick AG. 1927. A contribution to the mathematical theory of epidemics. Proc. R. Soc. A 115:700–21
    [Google Scholar]
  47. Khan MA, Rath KP, Yu H, Zhang Y. 2017. On the equivalence of large individualized and distributionalized games. Theor. Econ. 12:533–54
    [Google Scholar]
  48. Khan MA, Sun Y 2002. Non-cooperative games with many players. Handbook of Game Theory with Economic Applications 3 R Aumann, S Hart 1761–808 Amsterdam: Elsevier
    [Google Scholar]
  49. Lee S. 2016. Incentive compatibility of large centralized matching markets. Rev. Econ. Stud. 84:444–63
    [Google Scholar]
  50. Lipton RJ, Markakis E, Mehta A. 2003. Playing large games using simple strategies. Proceedings of the 4th ACM Conference on Electronic Commerce36–41 New York: ACM
    [Google Scholar]
  51. Milgrom PR, Weber RJ. 1985. Distributional strategies for games with incomplete information. Math. Oper. Res. 10:619–32
    [Google Scholar]
  52. Pelekis C, Ramon J 2017. Hoeffding's inequality for sums of dependent random variables. Mediterr. J. Math. 14:243
    [Google Scholar]
  53. Rashid S. 1983. Equilibrium points of non-atomic games: asymptotic results. Econ. Lett. 12:7–10
    [Google Scholar]
  54. Rubinstein A. 1991. Comments on the interpretation of game theory. Econometrica 59:909–24
    [Google Scholar]
  55. Sabourian H. 1990. Anonymous repeated games with a large number of players and random outcomes. J. Econ. Theory 51:92–110
    [Google Scholar]
  56. Schmeidler D. 1973. Equilibrium points of nonatomic games. J. Stat. Phys. 7:295–300
    [Google Scholar]
  57. Wooders M, Cartwright E, Selten R. 2006. Behavioral conformity in games with many players. Games Econ. Behav. 57:347–60
    [Google Scholar]
/content/journals/10.1146/annurev-economics-072720-042303
Loading

Supplementary Data

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error