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

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  • Weinstein, Jonathan
  • Yildiz, Muhamet

Abstract

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/inca/622836

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Keywords: Higher-order beliefs Incomplete information Robustness Sensitivity Universal type space;

References

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  1. Basu, Kaushik, 1992. "A characterization of the class of rationalizable equilibria of oligopoly games," Economics Letters, Elsevier, vol. 40(2), pages 187-191, October.
  2. R. Guesnerie, 2002. "Anchoring Economic Predictions in Common Knowledge," Econometrica, Econometric Society, vol. 70(2), pages 439-480, March.
  3. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  4. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
  5. Jonathan Weinstein & Muhamet Yildiz, 2004. "Finite-Order Implications of Any Equilibrium," Levine's Working Paper Archive 122247000000000065, David K. Levine.
  6. 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.
  7. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
  8. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
  9. Weinstein, Jonathan & Yildiz, Muhamet, 2007. "Impact of higher-order uncertainty," Games and Economic Behavior, Elsevier, vol. 60(1), pages 200-212, July.
  10. 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.
  11. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
  12. Penta, Antonio, 2013. "On the structure of rationalizability for arbitrary spaces of uncertainty," Theoretical Economics, Econometric Society, vol. 8(2), May.
  13. 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.
  14. 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.
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Cited by:
  1. Penta, Antonio, 2013. "On the structure of rationalizability for arbitrary spaces of uncertainty," Theoretical Economics, Econometric Society, vol. 8(2), May.
  2. Chen, Yi-Chun, 2012. "A structure theorem for rationalizability in the normal form of dynamic games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 587-597.

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