Bequest games with unbounded utility functions

The existence of Markov perfect equilibria for a deterministic bequest game with bounded from below utility function was established independently by Bernheim and Ray [2] and Leininger [8]. The aim of this paper is to provide a simpler proof that, in contrast to [2] and [8], also works for models with unbounded, e.g., isoelastic utility functions. Our approach employs the concept of strict single crossing property, introduced by Milgrom and Shannon in [10], and includes supermodular functions as special cases.