A key solution concept in cooperative game theory is the core. The core of an expense sharing game contains stable allocations of the total cost to the participating players, such that each subset of players pays at most what it would pay if acting on its own. Unfortunately, some expense sharing games have an empty core, meaning that the total cost is too high to be divided in a stable manner. ...

Spatial evolutionary games model individuals playing a game with their neighbors in a spatial domain and describe the time evolution of strategy profile of individuals over space. We derive integro-differential equations as deterministic approximations of strategy revision stochastic processes. These equations generalize the existing ordinary differential equations such as replicator dynamics a...

This paper proposes a structural life-cycle model to analyze the relationship between health risks, early retirement and saving behavior for employees in Germany. I rely on the framework of a dynamic programming discrete choice model with a discretized saving decision. The model accounts for both forward looking behavior and unobserved heterogeneity which is specified seminonparametrically. Hea...

The purpose of the course is to study several dynamics generated by strategic interactions in games. Among the topics are adaptive dynamics in evolutionary game theory, robust procedures for on-line algorithms and stochastic approximation. 1. Fictitious play Discrete time Continuous time and best reply dynamics 2. Replicator dynamics n populations One population Evolutionary Stable Strategies 3...

In this paper, we propose a novel modeling method, Stochastic Game Nets (SGN) and use it to model and analyze the attack actions in electronic commerce (ecommerce). Firstly, the definition and modeling algorithm of Stochastic Game Nets are given. And then we apply the Stochastic Game Nets method to describe the attack and defense course in e-commerce. Finally we analyze the attack time and atta...

We consider a class of fully stochastic and fully distributed algorithms, that we prove to learn equilibria in games. Indeed, we consider a family of stochastic distributed dynamics that we prove to converge weakly (in the sense of weak convergence for probabilistic processes) towards their mean-field limit, i.e an ordinary differential equation (ODE) in the general case. We focus then on a cla...

In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...