We propose two new signalling-game refinements that are microfounded in a model of patient Bayesian learning . Agents are born into player roles and play the signalling game against a random opponent each period. Inexperienced agents know their opponents' payoff functions but not the prevailing distribution of opponents' play . One refinement corresponds to an upper bound on the set of possible learning outcomes while the other provides a lower bound . Both refinements are closely related to divine equilibrium (Banks and Sobel, 1987) .
We show how to add the assumption that players know their opponents' payoff functions to the theory of learning in games, and use it to derive restrictions on signaling-game play in the spirit of divine equilibrium. In our learning model, agents are born into player roles and play the game against a random opponent each period. Inexperienced agents are uncertain about the prevailing distribution of opponents' play , and update their beliefs based on their observations. Long-lived and patient senders experiment with every signal that they think might yield an improvement over their myopically best play. We show that divine equilibrium (Banks and Sobel, 1987) is nested between "rationality-compatible" equilibrium, which corresponds to an upper bound on the set of possible learning outcomes , and "uniform rationality-compatible" equilibrium, which provides a lower bound .
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propose two new signalling-game refinements that are microfounded in a model of patient Bayesian learning . Agents
show how to add the assumption that players know their opponents' payoff functions to the theory of learning in games, and use it to derive restrictions on signaling-game play in the spirit of divine equilibrium. In our learning model, agents
D
signalling
R
know their opponents' payoff functions but not
are uncertain about
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. One refinement
, and update their beliefs based on their observations. Long-lived and patient senders experiment with every signal that they think might yield an improvement over their myopically best play. We show that divine equilibrium (Banks and Sobel, 1987) is nested between "rationality-compatible" equilibrium, which
R
while the other
, and "uniform rationality-compatible" equilibrium, which
D
. Both refinements are closely related to divine equilibrium (Banks and Sobel, 1987)