We study a class of discounted infinite horizon stochastic games with strategic complementarities. Using monotone operators on the space of values and strategies, we prove existence of a Stationary Markov Nash equilibrium under different set of assumptions than Curtat (1996), Amir (2002, 2005) or Nowak (2007) via constructive methods. In addition, we provide monotone comparative statics results...

We study the transition to phase synchronization in a model for the spread of infection defined in a small world network. It was shown [Phys. Rev. Lett. 86, 2909 (2001)] that the transition occurs at a finite degree of disorder p, unlike equilibrium models where systems behave as random networks even at infinitesimal p in the infinite-size limit. We examine this system under variation of a para...

In this paper we propose a dynamic model of Limit Order Book (LOB). The main feature of our model is that the shape of the LOB is determined endogenously by an expected utility function via a competitive equilibrium argument. Assuming zero resilience, the resulting equilibrium density of the LOB is random, nonlinear, and time inhomogeneous. Consequently, the liquidity cost can be defined dynami...

We study the dynamics of a system of N classical spins with infinite-range interaction. We show that, if the thermodynamic limit is taken before the infinite-time limit, the system does not relax to the Boltzmann-Gibbs equilibrium, but exhibits different equilibrium properties, characterized by stable non-Gaussian velocity distributions, Lévy walks, and dynamical correlation in phase space.

In this paper, we develop a family of high order asymptotic preserving schemes for some discrete-velocity kinetic equations under a diffusive scaling, that in the asymptotic limit lead to macroscopic models such as the heat equation, the porous media equation, the advectiondiffusion equation, and the viscous Burgers’ equation. Our approach is based on the micromacro reformulation of the kinetic...

When the stepsize in non-stii ODE codes is restricted by stability, an uneven pattern of stepsizes with many step rejections is frequently observed. Results analysing this behaviour have been obtained for Runge-Kutta methods, leading to several papers attempting to improve stepsize control. It is shown here that a similar analysis can be carried out for mul-tistep methods. The explicit Adams 2-...