Without equilibria, how do you decide what kind of agents to talk about? Random agents?
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I think you want some kind of rational agent constraint, still; recursive "common knowledge of rationality", even. Just refuse to accept arbitrary equilibria.
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Maybe accept unique equilibria when they exist. To first approximation, the idea is that agents are uncertain about what equilibrium they're in if there are several. This has obvious problems -- they're not in any equilibrium then, so why do they think they may be?
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What does it mean to have common knowledge that all players are "rational" without knowing what function they implement?
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Maybe you know that their function maximizes an expected utility, and you know their utility function, and you even know that there's a common prior between you wrt the game being played, but all you know about their beliefs about you is that they know those same things about you
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Because an infallible superbeing told you so?
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More like, because you were constructed for the purpose of being a convenient thought experiment.
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