Parikh: An Epistemic Generalization of Rationalizability
Abstract. Rationalizability, originally proposed by Bernheim and Pearce, generalizes the notion of Nash equilibrium. Nash equilibrium requires common knowledge of strategies. Rationalizability only requires common knowledge of rationality. However, their original notion assumes that the payoffs are common knowledge. I.e. agents do know what world they are in, but may be ignorant of what other agents are playing.
We generalize the original notion of rationalizability to consider situations where agents do not know what world they are in, or where some know but others do not know. Agents who know something about the world can take advantage of their superior knowledge. It may also happen that both Ann and Bob know about the world but Ann does not know that Bob knows. How might they act?
We will show how a notion of rationalizability in the context of partial knowledge, represented by a Kripke structure, can be developed.