The paper is concerned with the approximation of value function zero-sum differential game minimal cost, i.e., payoff functional determined by minimization some quantity along trajectory solutions continuous-time stochastic games stopping governed one player. Notice that auxiliary described Isaacs–Bellman equation additional inequality constraints. a parabolic PDE for case and it takes form sys...

We study an extraction site reclamation problem in a two-player differential game setting over finite time horizon. Environmental regulation requires each firm to engage efforts during the entire lifespan of and pay abandonment fee at end its lease term for unclaimed pollution caused by firms’ activities. Firms determine their order minimize cost. analyze compare individual choices stock noncoo...

<p style='text-indent:20px;'>This paper is concerned with a linear quadratic stochastic Stackelberg differential game time delay. The model general, in which the state delay and control both appear equation, moreover, they enter into diffusion term. By introducing two Pseudo-Riccati equations special matrix feedback representation of open-loop strategy derived, under some assumptions. Fin...

We apply the theoretical results on “stochastic approximations and differential inclusions” developed in Benäım, Hofbauer and Sorin (2005) to several adaptive processes used in game theory including: classical and generalized approachability, no-regret potential procedures (Hart and Mas-Colell), smooth fictitious play (Fudenberg and Levine).

The paper is devoted to the modelling of the propagation of acoustic waves at high frequency in anisotropic media. In this case, the WKB approximation results in eikonal equations whose Hamiltonians are neither convex nor concave in the impulse variable so that the Fermat principle fails. In this paper, methods of differential games are adopted for the analysis of wave propagation. If the Hamil...

We present upper-semicontinuity results for attractors and the chain-recurrent set of differential inclusions, in particular w.r.t. discretizations, and applications to game dynamics.