"Dense Types"

Stephen Morris

A strategic topology on higher order belief types says that two types are close if they behave in similar ways in similar situations. An upper (lower) strategic topology on types is the finest topology generating upper (lower) hemicontinuity of strategic outcomes. We show that the upper strategic topology is equivalent to the product topology and the lower strategic topology is strictly finer. Nonetheless, the set of "finite types" (types describable by finite type space) are dense in the lower strategic topology.