TITLE:
A Tree Formulation for Signaling Games with Noise
AUTHORS:
Xeni Dassiou, Dionysius Glycopantis
KEYWORDS:
Signals and Non-Cooperative Signaling Games, Noise, States of Nature, A Machine, Imperfect Information Sets, Actions, Language Convention, Nash Equilibrium, Beliefs Updating, Perfect Bayesian Equilibrium, Fixed Point, Self-Fulfilling Prophesies, Rational Expectations Equilibrium
JOURNAL NAME:
Natural Science,
Vol.6 No.13,
August
25,
2014
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.