Mixed Strategy Nash Equilibria in Signaling Games

Barry R. Cobb, Atin Basuchoudhary, Gregory Hartman

Department of Economics and Business, Virginia Military Institute, Lexington, USA.
Department of Mathematics and Computer Science, Virginia Military Institute, Lexington, USA.

DOI: 10.4236/tel.[phone]                

Abstract

Signaling games are characterized by asymmetric information where the more informed player has a choice about what information to provide to its opponent. In this paper, decision trees are used to derive Nash equilibrium strategies for signaling games. We address the situation where neither player has any pure strategies at Nash equilibrium, i.e. a purely mixed strategy equilibrium. Additionally, we demonstrate that this approach can be used to determine whether certain strategies are part of a Nash equilibrium containing dominated strategies. Analyzing signaling games using a decision-theoretic approach allows the analyst to avoid testing individual strategies for equilibrium conditions and ensures a perfect Bayesian solution.

Keywords

Game Theory; Decision Analysis; Decision Tree; Nash Equilibrium; Signaling Game

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. M. Spence, “Job Market Signaling,” Quarterly Journal of Economics, Vol. 87, No. 3, 1974, pp. 355-374. doi:10.2307/1882010
[2]	P. Milgrom and J. Roberts, “Limit Pricing and Entry Under Incomplete Information: An Equilibrium Analysis,” Econometrica, Vol. 50, No. 2, 1982, pp. 443-459. doi:10.2307/1912637
[3]	D. M. Kreps and J. Sobel, “Signalling,” In: R. J. Aumann and S. Hart, (Eds.), Handbook of Game Theory: With Economics Applications, Elsevier, Amsterdam, Vol. 2, No. 11, 1994, pp. 849-868.
[4]	J. G. Riley, “Silver Signals: Twenty-Five Years of Screening and Signaling,” Journal of Economic Literature, Vol. 39, No. 2, 2001, pp. 432-478. doi:10.1257/jel.39.2.432
[5]	B. von Stengel, “Equilibrium computation for Two-Player Games in Strategic and Extensive Form,” In: N. Nisan, T. Roughgarden, E. Tardos and V. V. Vazirani, (Eds.), Algorithmic Game Theory, Cambridge University Press, New York, 2007, pp. 53-78. doi:10.1017/CBO9780511800481.005
[6]	N. Nisan, T. Roughgarden, E. Tardos and V. V. Vazirani, “Algorithmic Game Theory,” Cambridge University Press, New York, 2007. doi:10.1017/CBO9780511800481
[7]	R. D. McKelvey, A. M. McLennan and T. Turocy, “Gambit: Software Tools for Game Theory, Version 0.2010.09.01,” 2011. http://www.gambit-project.org
[8]	D. Rios Insua, J. Rios and D. Banks, “Adversarial Risk Analysis,” Journal of the American Statistical Association, Vol. 104, No. 486, 2009, pp. 841-854. doi:10.1198/jasa.2009.0155
[9]	G. S. Parnell, C. M. Smith and F. I. Moxley, “Intelligent Adversary Risk Analysis: A Bioterrorism Risk Management Model,” Risk Analysis, Vol. 30, No. 1, 2010, pp. 32-48. doi:10.1111/j.1539-6924.2009.01319.x
[10]	E. Paté-Cornell and S. Guikema, “Probabilistic Modeling of Terrorist Threats: A Systems Analysis Approach to Setting Priorities among Countermeasures,” Military Operations Research, Vol. 7, No. 4, 2002, pp. 5-20. doi:10.5711/morj.7.4.5
[11]	D. Fudenberg and J. Tirole, “Game Theory,” MIT Press, Cambridge, 1993.
[12]	D. M. Kreps and R. Wilson, “Sequential Equilibria,” Econometrica, Vol. 50, No. 4, 1982, pp. 863-894. doi:10.2307/1912767
[13]	J. H. van Binsbergen and L. M. Marx, “Exploring Relations between Decision Analysis and Game Theory,” Decision Analysis, Vol. 4, No. 1, 2007, pp. 32-40. doi:10.1287/deca.1070.0084
[14]	B. R. Cobb and A. Basuchoudhary, “A Decision Analysis Approach to Solving the Signaling Game,” Decision Analysis, Vol. 6, No. 4, 2009, pp. 239-255. doi:10.1287/deca.1090.0148