Strong and safe Nash equilibrium in some repeated 3-player games

We consider a 3-player game in the normal form, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage players make their choices knowing only the average payoffs from previous stages of all the players. A strategy of a player in the repeated game is a function defined on the convex hull of the set of payoffs. Our aim is to construct a strong Nash equilibrium in the repeated game, i.e. a strategy profile being resistant to deviations by coalitions. Constructed equilibrium strategies are safe, i.e. the non-deviating player payoff is not smaller than the equilibrium payoff in the stage game, and deviating players' payoffs do not exceed the non-deviating player payoff more than a positive constant which can be arbitrary small and chosen by the non-deviating player. Our construction is inspired by Smale's good strategies described in \cite{smale}, where the repeated Prisoner's Dilemma was considered. In proofs we use arguments based on approachability and strong approachability type results.Comment: 19 page

EU and US Approaches to Delayed Access to Generic Drugs by Enforcement of a Patent or SPC Procured by Fraud

This article examines the impact of pharmaceutical patent protection on the introduction of generic drugs on the market. Basing itself on the Court of Justice of the European Union (CJEU) AstraZeneca case and US case law it examines, in particular, the way in which pharmaceutical companies may have created artificial barriers to entry for the market launch of generic drugs, so as to maintain market dominance by way of “life cycle management strategies”. Moreover, it compares the different ways, in which the EU and US have chosen to address the problem of the abuse of regulatory procedures by fraud with its purpose of delaying generic drug approvals. It also seeks to answer the question of whether the existence of a legal entitlement to a patent under the rules of patent law excludes competition-law liability.This article examines the impact of pharmaceutical patent protection on the introduction of generic drugs on the market. Basing itself on the Court of Justice of the European Union (CJEU) AstraZeneca case and US case law it examines, in particular, the way in which pharmaceutical companies may have created artificial barriers to entry for the market launch of generic drugs, so as to maintain market dominance by way of “life cycle management strategies”. Moreover, it compares the different ways, in which the EU and US have chosen to address the problem of the abuse of regulatory procedures by fraud with its purpose of delaying generic drug approvals. It also seeks to answer the question of whether the existence of a legal entitlement to a patent under the rules of patent law excludes competition-law liability

On the Lyapunov Second Method for Data Measurable in Time

In this paper the authors study time dependent Lyapunov functions for nonautonomous systems described by differential inclusions. In particular it is shown that Lyapunov functions are viscosity supersolutions of a Hamilton-Jacobi equation. For this aim a new viability theorem for differential inclusions with time dependent state constraints is proved. The viability conditions are formulated both using contingent cones and in a dual way, using subnormal cones (negative polar of contingent cone)

Parallel processors and nonlinear structural dynamics algorithms and software

The adaptation of a finite element program with explicit time integration to a massively parallel SIMD (single instruction multiple data) computer, the CONNECTION Machine is described. The adaptation required the development of a new algorithm, called the exchange algorithm, in which all nodal variables are allocated to the element with an exchange of nodal forces at each time step. The architectural and C* programming language features of the CONNECTION Machine are also summarized. Various alternate data structures and associated algorithms for nonlinear finite element analysis are discussed and compared. Results are presented which demonstrate that the CONNECTION Machine is capable of outperforming the CRAY XMP/14