How Restrictive Are Information Partitions?

Recently, several game theorists have questioned whether information partitions are appropriate. Bacharach (2005) has considered in particular more general information patterns which may not even correspond to a knowledge operator. Such patterns arise when agents lack perfect discrimination, as in Luce’s (1956) example of intransitive indifference. Yet after extending the state space to include what the agent knows, a modified information partition can still be constructed in a straightforward manner. The required modification introduces an extra set of impossible states into the partition. This allows a natural represention of the agent’s knowledge that some extended states are impossible. JEL Classification: C70, D80.