Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/201630
Authors: 
Dianetti, Jodi
Ferrari, Giorgio
Year of Publication: 
2019
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 605
Abstract: 
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 2 N, the players' admissible strategies to the set of Lipschitz processes with Lipschitz constant bounded by n. We prove that, for each n 2 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.
Subjects: 
nonzero-sum games
singular control
submodular games
Meyer-Zheng topology
maximum principle
Nash equilibrium
stochastic differential games
monotone-follower problem
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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