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.
Highlights
In this paper we use the Lewis [1] formulation of signaling and base our model on our earlier paper (Dassiou and Glycopantis [2]), where we analysed a signaling game using a decision tree formation
The earlier paper presents a number of Bayesian equilibria and explains which one is likely to prevail using as a criterion the expected payoffs that they entail for the two players
We have analysed a sequential game concerning instructions and decisions to and by players, where nature selects a state and a machine transmits a noisy signal which is received by a helper, H
Summary
In this paper we use the Lewis [1] formulation of signaling and base our model on our earlier paper (Dassiou and Glycopantis [2]), where we analysed a signaling game using a decision tree formation. Paper [2] departed from the assumption of a correct decision by the receiver leading to an optimal payoff for both It distinguished between true signals (by H ) and correct actions (by D ). Unlike [1], in our model a true signal is mutually rewarding if it leads to a correct decision by D but a correctly guessed state of nature by D is not necessarily so. A signal that no longer reflects the true state of nature will imply a zero payoff for H This is irrespective of whether or not it truthfully reflects the private information held by H and irrespective of whether D ’s actions are correct or not
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