Abstract
A natural way to relate the existence theorems of Reny (1999) and Simon and Zame (1990) would be to show the following: Each game with an endoge- nous sharing rule satisfying the assumptions of Simon and Zame (1990) is such that the payoff correspondence has a measurable selection inducing a normal- form game whose mixed extension satisfies the assumptions in Reny (1999). We present a result showing that this is not so in general, even not when the assumptions in Reny (1999) are weakened to those in Barelli and Meneghel (2013).