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Sensitivity of equilibrium behavior to higher-order beliefs in nice games

  • Weinstein, Jonathan
  • Yildiz, Muhamet

We analyze "nice" games (where action spaces are compact intervals, utilities continuous and strictly concave in own action), which are used frequently in classical economic models. Without making any "richness" assumption, we characterize the sensitivity of any given Bayesian Nash equilibrium to higher-order beliefs. That is, for each type, we characterize the set of actions that can be played in equilibrium by some type whose lower-order beliefs are all as in the original type. We show that this set is given by a local version of interim correlated rationalizability. This allows us to characterize the robust predictions of a given model under arbitrary common knowledge restrictions. We apply our framework to a Cournot game with many players. There we show that we can never robustly rule out any production level below the monopoly production of each firm.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 72 (2011)
Issue (Month): 1 (May)
Pages: 288-300

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Handle: RePEc:eee:gamebe:v:72:y:2011:i:1:p:288-300
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July.
  2. Börgers, Tilman & Janssen, Maarten C.W., 1995. "On the dominance solvability of large cournot games," Games and Economic Behavior, Elsevier, vol. 8(2), pages 297-321.
  3. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, 03.
  4. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
  5. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
  6. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
  7. Basu, Kaushik, 1992. "A characterization of the class of rationalizable equilibria of oligopoly games," Economics Letters, Elsevier, vol. 40(2), pages 187-191, October.
  8. Muhamet Yildiz & Jonathan Weinsten, 2004. "Impact of higher-order uncertainty," Econometric Society 2004 North American Winter Meetings 157, Econometric Society.
  9. Jonathan Weinstein & Muhamet Yildiz, 2004. "Finite-Order Implications of Any Equilibrium," Levine's Working Paper Archive 122247000000000065, David K. Levine.
  10. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
  11. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
  12. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
  13. Guesnerie, R., 1999. "Anchoring Economic Predictions in Common Knowledge," DELTA Working Papers 1999-06, DELTA (Ecole normale supérieure).
  14. Antonio Penta, 2008. "On the Structure of Rationalizability for Arbitrary Spaces of Uncertainty," PIER Working Paper Archive 09-021, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 05 Jun 2008.
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