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Rationalization in Signaling Games: Theory and Applications

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  • Pierpaolo Battigalli

Abstract

Focusing on signaling games, I illustrate the relevance of the rationalizability approach for the analysis multistage games with incomplete information. I define a class of iterative solution procedures, featuring a notion of “forward induction”: the Receiver tries to explain the Sender’s message in a way which is consistent with the Sender’s strategic sophistication and certain given restrictions on beliefs. The approach is applied to some numerical examples and economic models. In a standard model with verifiable messages a full disclosure result is obtained. In a model of job market signaling the best separating equilibrium emerges as the unique rationalizable outcome only when the high and low types are sufficiently different. Otherwise, rationalizability only puts bounds on the education choices of different types.

Suggested Citation

  • Pierpaolo Battigalli, 2004. "Rationalization in Signaling Games: Theory and Applications," Working Papers 275, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  • Handle: RePEc:igi:igierp:275
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    Cited by:

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    2. Pierpaolo Battigalli & Pietro Tebaldi, 2019. "Interactive epistemology in simple dynamic games with a continuum of strategies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(3), pages 737-763, October.
    3. Heifetz Aviad & Meier Martin & Schipper Burkhard C., 2021. "Prudent Rationalizability in Generalized Extensive-form Games with Unawareness," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 21(2), pages 525-556, June.
    4. Burkhard Schipper & Hee Yeul Woo, 2014. "Political Awareness, Microtargeting of Voters, and Negative Electoral Campaigning," Working Papers 148, University of California, Davis, Department of Economics.
    5. Pierpaolo Battigalli & Carlo Chiarella & Stefano Gatti & Tommaso Orlando, 2017. "M&A negotiations with limited information: how do opaque firms buy and get bought?," Working Papers 596, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
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    7. Li, Ying Xue & Schipper, Burkhard C., 2020. "Strategic reasoning in persuasion games: An experiment," Games and Economic Behavior, Elsevier, vol. 121(C), pages 329-367.
    8. Dominiak, Adam & Lee, Dongwoo, 2023. "Testing rational hypotheses in signaling games," European Economic Review, Elsevier, vol. 160(C).
    9. Schipper, Burkhard C. & Woo, Hee Yeul, 2019. "Political Awareness, Microtargeting of Voters, and Negative Electoral Campaigning," Quarterly Journal of Political Science, now publishers, vol. 14(1), pages 41-88, January.
    10. Weng, Xi & Wu, Fan & Yin, Xundong, 2023. "Linear Riley equilibria in quadratic signaling games," Journal of Economic Theory, Elsevier, vol. 213(C).
    11. Burkhard Schipper & Ying Xue Li, 2018. "Strategic Reasoning in Persuasion Games: An Experiment," Working Papers 181, University of California, Davis, Department of Economics.
    12. Burkhard Schipper & Hee Yeul Woo, 2012. "Political Awareness and Microtargeting of Voters in Electoral Competition," Working Papers 46, University of California, Davis, Department of Economics.
    13. Manili, Julien, 2024. "Order independence for rationalizability," Games and Economic Behavior, Elsevier, vol. 143(C), pages 152-160.

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    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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