Infinite-horizon non-zero-sum stochastic differential games with additive structure

Discount-sensitive equilibria in zero-sum stochastic differential games

“…Throughout this section, we work with a zerosum stochastic differential game with additive structure. The proof of Lemma 8.1 is based on a result in [18], which is an extension to zero-sum stochastic differential games of Lemma A.16 in Arapostathis and Borkar [1]. We next write in our present setting the theorems in [18], and then we verify that the hypotheses in these theorems indeed hold .…”

“…Studies stochastic differential games with additive structure (also known as separable; see e.g. [5,18,23]) to prove that bias optimality implies strong 0discount optimality. Moreover, using the vanishing discount technique, shows that a sequence of α-discount optimal strategies weakly converge to an average optimal strategy.…”

“…Next definition generalizes the concept of F-strong average given in [13] for discrete-time Markov control processes on Borel spaces. For this end, let J T (x, φ, ψ, r) be as in (18) with v ≡ r.…”

“…To obtain that bias optimality implies strong 0−discount optimality, in this section we work with a class of stochastic differential games with additive structure and bounded coefficients. This kind of games has been recently studied in [8,18,23]. The following additional assumption is required.…”

“…Using the convergence criterion given in [1] or [2], section 5 in [18] proves that the convergences φ m → φ, ψ m → ψ, α m → α, and h m → h, yield the following properties…”