We analyze the trade-off faced by authorities envisaging a one-shot structural re-form in a capitalistic industry. A structure is modeled as (1) a sharing of productive capital at some time and (2) a sharing of scarce sites or any other non-reproducible assets. These two distinct dimensions of...

We adopt a framework of vertical differentiation (i.e. differentiation by quality) to study the issue of Corporate Social Responsibility (CSR). We develop a model of duopoly in a two‐country setting, in which firms choose the country of location, the level of CSR and finally compete in the...

This article is devoted to a survey of results for differential games obtained through Viability Theory. We recall the basic theory for differential games (obtained in the 1990s), but we also give an overview of recent advances in the following areas : games with hard constraints, stochastic...

This paper is devoted to regret lower bounds in the classical model of stochastic multi-armed bandit. A well-known result of Lai and Robbins, which has then been extended by Burnetas and Katehakis, has established the presence of a logarithmic bound for all consistent policies. We relax the...

This paper deals with inertia functions in control theory introduced in Aubin, Bernardo and Saint-Pierre (2004, 2005) and their adaptation to dynamical games. The inertia function associates with any initial state-control pair the smallest of the worst norms over time of the velocities of the...

We study the existence of uniform correlated equilibrium payoffs in stochastic games. The correlation devices that we use are either autonomous (they base their choice of signal on previous signals, but not on previous states or actions) or stationary (their choice is independent of any data and...

We show on a 4x4 example that many dynamics may eliminate all strategies used in correlated equilibria, and this for an open set of games. This holds for the best-response dynamics, the Brown-von Neumann-Nash dynamics and any monotonic or weakly sign-preserving dynamics satisfying some standard...

This paper considers GARCH(1,1) models in which the time-varying coefficients are functions of the realizations of an exogenous stochastic process. Time series generated by this model are in general nonstationary. Necessary and sufficient conditions are given for the existence of non-explosive...

This paper studies the deviations of the regret in a stochastic multi-armed bandit problem. When the total number of plays n is known beforehand by the agent, Audibert et al. [2] exhibit a policy such that with probability at least 1−1/n, the regret of the policy is of order log n. They have...

We consider the problem of finding the minimal initial data of a controlled process which guarantees to reach a controlled target with a given probability of success or, more generally, with a given level of expected loss. By suitably increasing the state space and the controls, we show that...