In this paper, we establish the existence of Berge's strong equilibrium for games with n persons in infinite dimensional strategy spaces in the case where the payoff function of each player is quasi-concave. Moreover, we study the continuity of Berge's strong equilibrium correspondence and prove...

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

In this paper, we give new sufficient conditions for the existence of a solution of theg-maximum equality. As a consequence, we prove a new fixed point theorem. We also prove a new theorem of existence of Nash equilibrium.

In this paper, we investigate the existence of Berge–Zhukovskii equilibrium in general normal form games. We characterize its existence via the existence of a symmetric Nash equilibrium of some n-person subgame derived of the initial game. The significance of the obtained results is...

In this paper, we establish the existence of Berge's strong equilibrium for games with n persons in infinite dimensional space in the case where the payoff function of each player is quasi-concave. Moreover, we study the continuity of Berge's strong equilibria correspondence and essential games.

In this paper, we study the main properties of the strong Berge equilibrium which is also a Pareto efficient (SBPE) and the strong Nash equilibrium (SNE). We prove that any SBPE is also a SNE, we prove also existence theorem of SBPE based on the KyFan inequality. Finally, we also provide a...

We establish some elementary results on solutions to the Bellman equation without introducing any topological assumption. Under a small number of conditions, we show that the Bellman equation has a unique solution in a certain set, that this solution is the value function, and that the value...

Let E be a real reflexive strictly convex Banach space which has uniformly Gâteaux differentiable norm. Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathcal{S}=\{T(s): 0 \leq s \infty\}}$$</EquationSource> </InlineEquation> be a nonexpansive semigroup on E such that <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${Fix(\mathcal{S}) := \cap_{t\geq 0}Fix( T(t) ) \not= \emptyset}$$</EquationSource> </InlineEquation> , and f is a contraction on...</equationsource></inlineequation></equationsource></inlineequation>

The primary aim of this article is to resolve a global optimization problem in the setting of a partially ordered set that is equipped with a metric. Indeed, given non-empty subsets A and B of a partially ordered set that is endowed with a metric, and a non-self mapping <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${S : A \longrightarrow...</equationsource></inlineequation>