TY  - GEN
AB  - We consider a class of N-player stochastic games of multi-dimensional singular
control, in which each player faces a minimization problem of monotone-follower type with
submodular costs. We call these games monotone-follower games. In a not necessarily
Markovian setting, we establish the existence of Nash equilibria. Moreover, we introduce
a sequence of approximating games by restricting, for each n ∈ ℕ, the players' admissible
strategies to the set of Lipschitz processes with Lipschitz constant bounded by n. We prove
that, for each n ∈ ℕ, there exists a Nash equilibrium of the approximating game and that the
sequence of Nash equilibria converges, in the Meyer-Zheng sense, to a weak (distributional)
Nash equilibrium of the original game of singular control. As a byproduct, such a convergence
also provides approximation results of the equilibrium values across the two classes of games.
We finally show how our results can be employed to prove existence of open-loop Nash
equilibria in an N-player stochastic differential game with singular controls, and we propose
an algorithm to determine a Nash equilibrium for the monotone-follower game.
DA  - 2019
KW  - nonzero-sum games
KW  - singular control
KW  - submodular games
KW  - Meyer-Zheng topology
KW  - maximum principle
KW  - Nash equilibrium
KW  - stochastic differential games
KW  - monotone-follower problem.
LA  - eng
PY  - 2019
SN  - 0931-6558
TI  - Nonzero-Sum Submodular Monotone-Follower Games. Existence and Approximation of Nash Equilibria
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29329948
Y2  - 2024-11-22T01:25:12
ER  -