A controller and a stopper game with degenerate variance control.
A dynamic model of advertising competition: an empirical analysis of feedback strategies
A gradient-type algorithm for the numerical solution of two-player zero-sum differential game problems
A maximum principle approach to risk indifference pricing with partial information.
A new Logistical Approach to Management of Export/Import Operations in a National Economics.
Analytic solution of Riccati equations occurring in open-loop Nash multiplayer differential games.
Boundary-influenced robust controls: two network examples
We consider the differential game associated with robust control of a system in a compact state domain, using Skorokhod dynamics on the boundary. A specific class of problems motivated by queueing network control is considered. A constructive approach to the Hamilton-Jacobi-Isaacs equation is developed which is based on an appropriate family of extremals, including boundary extremals for which the Skorokhod dynamics are active. A number of technical lemmas and a structured verification theorem...
Brève communication. Méthode de l'état adjoint par «relaxation»
Completing linear differential games by state dependent strategies
Convergence method, properties and computational complexity for Lyapunov games
We introduce the concept of a Lyapunov game as a subclass of strictly dominated games and potential games. The advantage of this approach is that every ergodic system (repeated game) can be represented by a Lyapunov-like function. A direct acyclic graph is associated with a game. The graph structure represents the dependencies existing between the strategy profiles. By definition, a Lyapunov-like function monotonically decreases and converges to a single Lyapunov equilibrium point identified by...
Differential Games and Nonlinear First Order PDE on Bounded Domains.
Discretized feedback for differential games
Existence of the value of fixed duration dynamical games [Book]
Feedback Nash equilibria in optimal taxation problems
A well-known result in public economics is that capital income should not be taxed in the long run. This result has been derived using necessary optimality conditions for an appropriate dynamic Stackelberg game. In this paper we consider three models of dynamic taxation in continuous time and suggest a method for calculating their feedback Nash equilibria based on a sufficient condition for optimality. We show that the optimal tax on capital income is generally different from zero.
From optimal control to non-cooperative differential games: a homotopy approach
Growth versus environment in dynamic models of capital accumulation.
Hamilton–Jacobi equations and two-person zero-sum differential games with unbounded controls
A two-person zero-sum differential game with unbounded controls is considered. Under proper coercivity conditions, the upper and lower value functions are characterized as the unique viscosity solutions to the corresponding upper and lower Hamilton–Jacobi–Isaacs equations, respectively. Consequently, when the Isaacs’ condition is satisfied, the upper and lower value functions coincide, leading to the existence of the value function of the differential game. Due to the unboundedness of the controls,...
Jeux différentiels et approximation numérique de fonctions valeur. 1re partie : étude théorique
Jeux différentiels et approximation numérique de fonctions valeur. 2e partie : étude numérique