A single-state epistemic model can satisfy common knowledge of rationality if the state space is constructed so that each player's strategy is optimal given the probability-one beliefs held at that state.
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common knowledge of rationality(Epistemic game theory)
An epistemic condition in which all players are rational, all players know all players are rational, all players know that all players know all players are rational, and so on ad infinitum
epistemic model(Epistemic game theory)
A formal structure assigning strategy profiles to possible worlds/states, here containing a single state w
knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.
strategy(Logic of strategies / propositional dynamic logic)
A program that instructs an agent on how to navigate a game tree, potentially recommending one or more actions at each turn; strategies may remain partial, resembling plans.