In the teaching of dynamic games with incomplete information, the solution of perfect Bayesian equilibrium is a difficult point. Although there is no general solution to the general dynamic games with incomplete information, there is a general solution method to the signaling games. Most of the existing game theory textbooks do not give clear solving methods and specific calculation steps. This paper analyses how to calculate the perfect Bayesian equilibrium of an extensive-form signaling game through an example. In this paper, Gibbons' definition of perfect Bayesian equilibrium is taken as the definition of perfect Bayesian equilibrium. The definition attaches four requirements to Nash equilibrium. That is, in a dynamic game with incomplete information, the Nash equilibrium satisfying these four requirements is a perfect Bayesian equilibrium. The calculation process is divided into 4 steps. First, the belief hypothesis. Second, analysis of the signal receiver’s strategy and the requirements for the posterior probability. Third, analysis of the signal sender’s behavior according to different belief combinations. Finally, the posterior probabilities are analyzed using the requirements 3 and 4 in the perfect Bayesian equilibrium definition. On the basis of the previous analyses, the perfect Bayesian equilibria of the signaling game can be calculated step by step.
| Published in | Higher Education Research (Volume 8, Issue 4) |
| DOI | 10.11648/j.her.20230804.20 |
| Page(s) | 193-200 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Signaling Game, Perfect Bayesian Equilibrium (PBE), Requirement, Strategy, Belief
| [1] | Weiying Zhang. (2004). Game Theory and Information Economics. Shanghai People's Publishing House, Shanghai. |
| [2] | Guangming Hou and Cunjin Li. (2005). Managerial Game Theory. Beijing Institute of Technology Press, Beijing. |
| [3] | Gibbons R. (1992). Game Theory for Applied Economists. Princeton University Press, Princeton. |
| [4] | Fudenberg D. and J. Tirole. (1991). Perfect Bayesian equilibrium and sequential equilibrium, Journal of Economic Theory. Vol. 53 No. 2, pp. 236-260. |
| [5] | Osborne M. J. and Rubinstein A.. (1994). A Course in Game Theory. MIT Press, Cambridge, MA. |
| [6] | Dutta P. K. (1999). Strategies and Games: Theory and Practice. MIT Press Cambridge, MA. |
| [7] | Shiyu Xie. (2017). Game Theory in Economics. Fudan University Press, Shanghai. |
| [8] | Changde Zheng. (2018). Game Theory and its Application in Economic Management. Economic Press China. |
| [9] | Fudenberg D. and J. Tirole. (1991). Game Theory. MIT Press, Cambridge, MA. |
| [10] | Giacomo Bonanno. (2013). AGM-consistency and perfect Bayesian equilibrium. Part I: definition and properties. International Journal of Game Theory. Vol. 42 No. 3, pp. 567-592. |
| [11] | Julio González-Díaz and Miguel A Meléndez-Jiménez. (2014). On the notion of perfect Bayesian equilibrium. TOP. Vol. 22 No. 1, pp. 128-143. |
| [12] | Steven T. (2013). Game Theory: an Introduction. Princeton University Press, Princeton. |
| [13] | Peters H. (2015). Game Theory: a Multi-Leveled Approach. Springer, Heidelberg. |
| [14] | Rasmusen E. (2007). Games and Information: an Introduction to Game Theory. Basil Blackwell, Cambridge, MA. |
| [15] | J. Tirole (1988). The Theory of Industrial Organization. MIT Press, Cambridge, MA. |
APA Style
Yuming Xiao. (2023). Calculation of Perfect Bayesian Equilibrium in a Signaling Game. Higher Education Research, 8(4), 193-200. https://doi.org/10.11648/j.her.20230804.20
ACS Style
Yuming Xiao. Calculation of Perfect Bayesian Equilibrium in a Signaling Game. High. Educ. Res. 2023, 8(4), 193-200. doi: 10.11648/j.her.20230804.20
AMA Style
Yuming Xiao. Calculation of Perfect Bayesian Equilibrium in a Signaling Game. High Educ Res. 2023;8(4):193-200. doi: 10.11648/j.her.20230804.20
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Download@article{10.11648/j.her.20230804.20,
author = {Yuming Xiao},
title = {Calculation of Perfect Bayesian Equilibrium in a Signaling Game},
journal = {Higher Education Research},
volume = {8},
number = {4},
pages = {193-200},
doi = {10.11648/j.her.20230804.20},
url = {https://doi.org/10.11648/j.her.20230804.20},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.her.20230804.20},
abstract = {In the teaching of dynamic games with incomplete information, the solution of perfect Bayesian equilibrium is a difficult point. Although there is no general solution to the general dynamic games with incomplete information, there is a general solution method to the signaling games. Most of the existing game theory textbooks do not give clear solving methods and specific calculation steps. This paper analyses how to calculate the perfect Bayesian equilibrium of an extensive-form signaling game through an example. In this paper, Gibbons' definition of perfect Bayesian equilibrium is taken as the definition of perfect Bayesian equilibrium. The definition attaches four requirements to Nash equilibrium. That is, in a dynamic game with incomplete information, the Nash equilibrium satisfying these four requirements is a perfect Bayesian equilibrium. The calculation process is divided into 4 steps. First, the belief hypothesis. Second, analysis of the signal receiver’s strategy and the requirements for the posterior probability. Third, analysis of the signal sender’s behavior according to different belief combinations. Finally, the posterior probabilities are analyzed using the requirements 3 and 4 in the perfect Bayesian equilibrium definition. On the basis of the previous analyses, the perfect Bayesian equilibria of the signaling game can be calculated step by step.},
year = {2023}
}
TY - JOUR T1 - Calculation of Perfect Bayesian Equilibrium in a Signaling Game AU - Yuming Xiao Y1 - 2023/08/31 PY - 2023 N1 - https://doi.org/10.11648/j.her.20230804.20 DO - 10.11648/j.her.20230804.20 T2 - Higher Education Research JF - Higher Education Research JO - Higher Education Research SP - 193 EP - 200 PB - Science Publishing Group SN - 2578-935X UR - https://doi.org/10.11648/j.her.20230804.20 AB - In the teaching of dynamic games with incomplete information, the solution of perfect Bayesian equilibrium is a difficult point. Although there is no general solution to the general dynamic games with incomplete information, there is a general solution method to the signaling games. Most of the existing game theory textbooks do not give clear solving methods and specific calculation steps. This paper analyses how to calculate the perfect Bayesian equilibrium of an extensive-form signaling game through an example. In this paper, Gibbons' definition of perfect Bayesian equilibrium is taken as the definition of perfect Bayesian equilibrium. The definition attaches four requirements to Nash equilibrium. That is, in a dynamic game with incomplete information, the Nash equilibrium satisfying these four requirements is a perfect Bayesian equilibrium. The calculation process is divided into 4 steps. First, the belief hypothesis. Second, analysis of the signal receiver’s strategy and the requirements for the posterior probability. Third, analysis of the signal sender’s behavior according to different belief combinations. Finally, the posterior probabilities are analyzed using the requirements 3 and 4 in the perfect Bayesian equilibrium definition. On the basis of the previous analyses, the perfect Bayesian equilibria of the signaling game can be calculated step by step. VL - 8 IS - 4 ER -
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