Necessary and Sufficient Optimality Conditions for Regular–Singular Stochastic Differential Games with Asymmetric Information

Wang, Yan; Wang, Lei; Teo, Kok Lay

doi:10.1007/s10957-018-1251-3

Cited by 8 publications

(3 citation statements)

References 26 publications

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“…Singular zero-sum differential games were extensively studied in the literature in both, undelayed and delayed dynamics, settings (see, e.g., [9,12,16,17,18,19,20,21,22,23,24,25] and references therein). Singular Nash equilibrium differential games also were considered in the literature, but mostly in various stochastic settings (see, e.g., [15,26,27,28,29] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Solutions of one class of singular two-person Nash equilibrium games with state and control delays: Regularization approach

2023

Appl. Set-Valued Anal. Optim.

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In this paper, a finite-horizon two-person Nash equilibrium game for a linear time-dependent differential system with delays (point-wise and distributed) in the state variable and the players' control variables is considered. The behaviour of each player is evaluated by its own quadratic functional to be minimized by this player. The feature of this game is that a weight matrix of the control in the functional of one player is singular (but, in general, non-zero). Due to this feature, the game itself is singular. Using the regularization method and the asymptotic analysis of the regularized Nash equilibrium game, an open-loop Nash equilibrium solution to the considered singular game is derived. Illustrative example is presented. Along with this example, two examples on non-uniqueness of open-loop Nash equilibrium solutions to the singular game are presented.

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Section: Introductionmentioning

confidence: 99%

Solutions of one class of singular two-person Nash equilibrium games with state and control delays: Regularization approach

2023

Appl. Set-Valued Anal. Optim.

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“…The number of contributions on games of singular controls is still quite limited (see [19], [22], [26], [27], [36], [45], [51]), although these problems have received an increasing interest in the recent years. We briefly discuss here some of these works.…”

Section: Introductionmentioning

confidence: 99%

“…Such a problem has been motivated by a question arising in public economic theory. A general characterization of Nash equilibria through the Pontryagin Maximum Principle approach has been investigated in the recent [51] for regular-singular stochastic differential games. Connections between nonzero-sum games of singular control and games of optimal stopping have been tackled in [19].…”

Section: Introductionmentioning

confidence: 99%

Nonzero-Sum Submodular Monotone-Follower Games: Existence and Approximation of Nash Equilibria

Dianetti¹,

Ferrari²

2018

Preprint

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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.

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Linear-quadratic-singular stochastic differential games and applications

Dianetti

2023

Decisions Econ Finan

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Necessary and Sufficient Optimality Conditions for Regular–Singular Stochastic Differential Games with Asymmetric Information

Cited by 8 publications

References 26 publications

Solutions of one class of singular two-person Nash equilibrium games with state and control delays: Regularization approach

Solutions of one class of singular two-person Nash equilibrium games with state and control delays: Regularization approach

Nonzero-Sum Submodular Monotone-Follower Games: Existence and Approximation of Nash Equilibria

Linear-quadratic-singular stochastic differential games and applications

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