Predictions under common knowledge of payoffs may differ from those under arbitrarily, but finitely, many orders of mutual knowledge; Rubinstein's (1989)Email game is a seminal example. Weinstein and Yildiz (2007) showed that the discontinuity in the example generalizes: for all types with...

For a finite set of actions and a rich set of fundamentals, consider the rationalizable actions on a universal type space, endowed with the usual product topology. (1) Generically, there exists a unique rationalizable action profile. (2) Every model can be approximately embedded in a...