NS  Vol.6 No.13 , August 2014
A Tree Formulation for Signaling Games with Noise
Abstract: The paper provides an analysis of a sender-receiver sequential signaling game. The private information of the sender is transmitted with noise by a Machine, i.e. does not always correctly reflect the state of nature. Hence, a truthful revelation by the sender of his information does not necessarily imply that the signal he sends is correct. Also, the receiver can take a correct action even if the sender transmits an incorrect signal. The payoffs of the two players depend on their combined actions. Perfect Bayesian Equilibria which can result from different degrees of noise is analysed. The Bayesian updating of probabilities is explained. The fixed point theorem which makes the connection with the idea of rational expectations in economics is calculated. Given a number of equilibria, we comment on the most credible one on the basis of the implied payoffs for both players. The equilibrium signals are an example of the formation of a language convention discussed by D. Lewis.
Cite this paper: Dassiou, X. and Glycopantis, D. (2014) A Tree Formulation for Signaling Games with Noise. Natural Science, 6, 1128-1139. doi: 10.4236/ns.2014.613101.

[1]   Lewis, D. (1969) Convention. Harvard University Press, Cambridge, MA.

[2]   Dassiou, X. and Glycopantis, D. (2013) A Tree Formulation for Signaling Games. Game Theory, 2013, Article ID: 754398, 12p.

[3]   Blume, A. (2012) A Class of Strategy-Correlated Equilibria in Sender-Receiver Games. Games and Economic Behavior, 75, 510-517.

[4]   Rubinstein, A. (2000) Economics and Language. Cambridge University Press, Cambridge, UK.

[5]   Cho, I. and Kreps, D.M. (1987) Signaling Games and Stable Equilibria. The Quarterly Journal of Economics, 102, 179-221.

[6]   Pawlowitsch, C. (2008) Why Evolution Does Not Always Lead to an Optimal Signaling System. Games and Economic Behavior, 63, 203-226.

[7]   Huttegger, S.M. (2007) Evolutionary Explanations of Indicatives and Imperatives. Erkenntnis, 66, 409-436.

[8]   Skyrms, B. (2010) The Flow of Information in Signaling Games. Philosophical Studies, 147, 155-165.

[9]   Stokke, A. (2014) Truth and Context Change. Journal of Philosophical Logic, 43, 33-51.

[10]   Glycopantis, D., Muir, A. and Yannelis, N. (2003) On Extensive form Implementation of Contracts in Differential Information Economies. Economic Theory, 21, 495-526. (Reprinted in Aliprantis, C.D., Arrow, K.J., et al., Eds., Assets, Beliefs, and Equilibria in Economic Dynamics, Springer-Verlag, 2004, 323-354.)