Nonzero-sum submodular monotone-follower games: Existence and approximation of Nash equilibria

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Center for Mathematical Economics Working Papers ; No. 605

Classification and Topics

• Classification: Wirtschaft
• Subject: nonzero-sum games ; singular control ; submodular games ; Meyer-Zheng topology ; maximum principle ; Nash equilibrium ; stochastic differential games ; monotone-follower problem

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Dianetti, Jodi ; Ferrari, Giorgio
• Event: Veröffentlichung
• (who): Bielefeld University, Center for Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2019

Further information

• Handle: http://hdl.handle.net/10419/201630
• URN: urn:nbn:de:0070-pub-29329948
• Last update: 10.03.2025, 11:44 AM CET