1 research outputs found
Minimax representation of nonexpansive functions and application to zero-sum recursive games
We show that a real-valued function on a topological vector space is
positively homogeneous of degree one and nonexpansive with respect to a weak
Minkowski norm if and only if it can be written as a minimax of linear forms
that are nonexpansive with respect to the same norm. We derive a representation
of monotone, additively and positively homogeneous functions on
spaces and on , which extend results of Kolokoltsov, Rubinov,
Singer, and others. We apply this representation to nonconvex risk measures and
to zero-sum games. We derive in particular results of representation and
polyhedral approximation for the class of Shapley operators arising from games
without instantaneous payments (Everett's recursive games)