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 .
We add the assumption that players know their opponents' payoff functions and rationality to a model of non-equilibrium learning in signaling games. Agents are born into player roles and play against random opponents every period. Inexperienced agents are uncertain about the prevailing distribution of opponents' play, but believe that opponents never choose conditionally dominated strategies. Agents engage in active learning and update beliefs based on personal observations. Payoff information can refine or expand learning predictions, since patient young senders' experimentation incentives depend on which receiver responses they deem plausible . We show that with payoff knowledge, the limiting set of long-run learning outcomes is bounded above by rationality-compatible equilibria (RCE), and bounded below by uniform RCE. RCE refine the Intuitive Criterion (Cho and Kreps, 1987) and include all divine equilibria (Banks and Sobel, 1987) . Uniform RCE sometimes but not always exists, and implies universally divine equilibrium .
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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
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but believe that opponents never choose conditionally dominated strategies. Agents engage in active learning and update
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their observations. Long-lived and patient senders experiment with every signal that they think might yield an improvement over their myopically best play
personal observations. Payoff information can refine or expand learning predictions, since patient young senders' experimentation incentives depend on which receiver responses they deem plausible
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divine equilibrium
with payoff knowledge, the limiting set of long-run learning outcomes is bounded above by rationality-compatible equilibria (RCE), and bounded below by uniform RCE. RCE refine the Intuitive Criterion (Cho and Kreps, 1987) and include all divine equilibria
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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
. Uniform RCE sometimes but not always exists, and implies universally divine equilibrium