Summary: We present an alternative proof of an existence result for Bayesian games (or games with differential information) given by T. Kim and N. C. Yannelis [J. Econ. Theory 77, No. 2, 330-353 (1998; Zbl 0896.90183)]. The result we provide is identical to Theorem 4.1 in this paper. However, not only the present argument is different, but it also has the advantage that it follows the footsteps of the argument given by N. C. Yannelis and N. D. Prabhakar [J. Math. Econ. 12, 233-245 (1983; Zbl 0536.90019)] and therefore it can be used to generalize the Kim-Yannelis theorem to abstract Bayesian economies. Our argument combines several measure theoretic and functional analytic results. In particular, we employ a Carathéodory type selection theorem, a result on weak compactness (known as Diestel’s theorem), the Fatou lemma in infinite-dimensional spaces, and the Fan-Glicksberg fixed point theorem.
For the entire collection see [Zbl 0893.00033].