The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Large Games (Structural Robustness)

  • Ehud Kalai
Reference work entry


In strategic games with many semi-anonymous players all the equilibria are structurally robust. The equilibria survive under structural alterations of the rules of the game and its information structure, even when the game is embedded in bigger games. Structural robustness implies ex post Nash conditions and a stronger condition of information-proofness. It also implies fast learning, self-purification and strong rational expectations in market games. Structurally robust equilibria may be used to model games with highly unspecified structures, such as games played on the web.


Herding Large games Mixed-strategy equilibrium Pure-strategy equilibrium Purification Rational expectations equilibrium Structural robustness 

JEL Classifications

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  1. Aumann, R.J., and L.S. Shapley. 1974. Values of nonatomic games. Princeton: Princeton University Press.Google Scholar
  2. Bergemann, D., and S. Morris. 2005. Robust mechanism design. Econometrica 73: 1771–1813.CrossRefGoogle Scholar
  3. Cremer, J., and R.P. McLean. 1985. Optimal selling strategies under uncertainty for a discriminating monopolist when demands are interdependent. Econometrica 53: 345–361.CrossRefGoogle Scholar
  4. Dubey, P., and J. Geanakoplos. 2003. From Nash to Walras via Shapley–Shubik. Journal of Mathematical Economics 39: 391–400.CrossRefGoogle Scholar
  5. Dubey, P., and M. Kaneko. 1984. Information patterns and Nash equilibria in extensive games: 1. Mathematical Social Sciences 8: 111–139.CrossRefGoogle Scholar
  6. Dubey, P., A. Mas-Colell, and M. Shubik. 1980. Efficiency properties of strategic market games: An axiomatic approach. Journal of Economic Theory 22: 339–362.CrossRefGoogle Scholar
  7. Green, J.R., and J.J. Laffont. 1987. Posterior implementability in a two-person decision problem. Econometrica 55: 69–94.CrossRefGoogle Scholar
  8. Kalai, E. 2004. Large robust games. Econometrica 72: 1631–1666.CrossRefGoogle Scholar
  9. Kalai, E. 2005. Partially-specified large games. Lecture Notes in Computer Science 3828: 3–13.CrossRefGoogle Scholar
  10. Kalai, E., and E. Lehrer. 1993. Rational learning leads to Nash equilibrium. Econometrica 61: 1019–1045.CrossRefGoogle Scholar
  11. Khan, A.M., and Y. Sun. 2002. Non-cooperative games with many players. In Handbook of game theory with economic applications, ed. R.J. Aumann and S. Hart, Vol. 3. Amsterdam: North-Holland.Google Scholar
  12. McLean, R., J. Peck, and A. Postlewaite. 2005. On price-taking behavior in asymmetric information economies. In Essays in dynamic general equilibrium: Festschrift for David Cass, ed. A. Citanna, J. Donaldson, H. Polemarchakis, P. Siconolfi, and S. Spear. Berlin: Springer. Repr. in Studies in Economic Theory 20:129–142.Google Scholar
  13. Rustichini, A., M.A. Satterthwaite, and S.R. Williams. 1994. Convergence to efficiency in a simple market with incomplete information. Econometrica 62: 1041–1064.CrossRefGoogle Scholar
  14. Schmeidler, D. 1973. Equilibrium points of nonatomic games. Journal of Statistical Physics 17: 295–300.CrossRefGoogle Scholar
  15. Shapley, L.S., and M. Shubik. 1977. Trade using one commodity as a means of payment. Journal of Political Economy 85: 937–968.CrossRefGoogle Scholar
  16. Wilson, R. 1987. Game-theoretic analyses of trading processes. In Advances in economic theory: Fifth world congress, ed. T. Bewley. Cambridge: Cambridge University Press.Google Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Ehud Kalai
    • 1
  1. 1.