One answers to an open question of Herings et al. (2008), by proving that their fixed point theorem for discontinuous functions works for mappings defined on convex compact subset of $\R^n$, and not only polytopes. This fixed point theorem can be applied to the problem of Nash equilibrium...

One answers to an open question of Herings et al. (2008), by proving that their fixed point theorem for discontinuous functions works for mappings defined on convex compact subset of a Euclidean space, and not only polytopes. This rests on a fixed point result of Toussaint

This paper investigates the existence of pure strategy, dominant-strategy, and mixed strategy Nash equilibria in discontinuous and nonconvex games. We introduce a new notion of very weak continuity, called weak transfer continuity, which holds in a large class of discontinuous economic games and...

In a recent but well known paper, Reny has proved the existence of Nash equilibria for compact and quasiconcave games, with possibly discontinuous payoff functions. In this paper, we prove that the quasiconcavity assumption in Reny's theorem can be weakened : we introduce a measure allowing to...

In a recent but well known paper, Reny has proved the existence of Nash equilibria for compact and quasiconcave games, with possibly discontinuous payoff functions. In this paper, we prove that the quasiconcavity assumption in Reny's theorem can be weakened : we introduce a measure allowing to...

There are several approaches of sharing resources among users. There is a noncooperative approach wherein each user strives to maximize its own utility. The most common optimality notion is then the Nash equilibrium. Nash equilibria are generally Pareto inefficient. On the other hand, we...

A sufficient and necessary condition is presented for the existence of a Nash equilibrium in n-person noncooperative games in normal form where strategy sets are not necessarily convex. Under the convexity condition, we show that this new sufficient and necessary condition is a particular case...

This article establishes the prevalence of deterrence over preemption when targeted governments can choose between either policies or employ both. There is a similar proclivity to favor defensive counter-terrorist measures over proactive policies. Unfortunately, this predisposition results in an...

There are several approaches of sharing resources among users. There is a noncooperative approach wherein each user strives to maximize its own utility. The most common optimality notion is then the Nash equilibrium. Nash equilibria are generally Pareto inefficient. On the other hand, we...