Value?based distance between information structures

We define the distance between two information structures as largest possible difference in value across all zero?sum games. provide a tractable characterization of and use it to discuss relation games versus single?agent problems, additional information, informational substitutes, complements, or joint information. The convergence countable structure under value?based is equivalent weak belief hierarchies, implying, among other things, that for games, approximate knowledge common knowledge. At same time, space large: there exists sequence where players acquire increasingly more ? > 0 such any elements have at least . This result answers by negative second (and last unsolved) three problems posed Mertens his paper “Repeated Games” (1986).