Rabia Nessah

A note on the existence of Berge and Berge–Nash equilibria

This paper deals with the problem of existence of Berge and Berge-Nash equilibria. Abalo and Kostreva have proved existence theorems of Berge and Berge-Nash equilibria for S-equi-well-posed and (S, [sigma])-equi-well-posed games, namely, Theorems 3.2-3.3 [Abalo, K.Y., Kostreva, M.M., 1996. Fixed Points, Nash Games and their Organization. Topological Methods in Nonlinear Analysis 8, 205-215.]. In this paper we show that the assumptions of these theorems are actually not sufficient for the existence of Berge equilibrium. We then propose a new version of these theorems.

Branch-and-bound method for minimizing the weighted completion time scheduling problem on a single machine with release dates

In this paper, we consider a single-machine scheduling problem with release dates. The aim is to minimize the total weighted completion time. This problem is known to be strongly NP-hard. We propose two new lower bounds that can be, respectively, computed in O(n2) and in O ( n log n ) time where n is the number of jobs. We prove a sufficient and necessary condition for local optimality, which can also be considered as a priority rule. We present an efficient heuristic using such a condition. We also propose some dominance properties. A branch-and-bound algorithm incorporating the heuristic, the lower bounds and the dominance properties is proposed and tested on a large set of instances. Highlights? In this paper, we consider a single machine scheduling problem with release dates. ? We propose two new lower bounds that can be, respectively, computed in O ( n 2 ) and in O ( n ln n ) . ? We present a new efficient heuristic which is complementary with the existence results. ? We propose some dominance properties and a branch-and-bound algorithm capable of solving problems with up to 120 jobs.

HOW TO PLAY GAMES? NASH VERSUS BERGE BEHAVIOUR RULES

Social interactions regularly lead to mutually beneficial transactions that are sometimes puzzling. The prisoner’s dilemma and the chicken and trust games prove to be less perplexing than Nash equilibrium predicts. Moral preferences seem to complement self-oriented motivations and their relative predominance in games is found to vary according to the individuals, their environment, and the game. This paper examines the appropriateness of Berge equilibrium to study several 2×2 game situations, notably cooperative games where mutual support yields socially better outcomes. We consider the Berge behavior rule complementarily to Nash: individuals play one behavior rule or another, depending on the game situation. We then define non-cooperative Berge equilibrium, discuss what it means to play in this fashion, and argue why individuals may choose to do so. Finally, we discuss the relationship between Nash and Berge notions and analyze the rationale of individuals playing in a situational perspective.

An exact method for problem

This paper addresses an identical parallel machine scheduling problem, with sequence-dependent setup times and release dates to minimize total completion time. This problem is known to be strongly NP-hard. We prove a sufficient and necessary condition for local optimality which can also be considered as a priority rule. We then define a dominant subset based on this condition. We present efficient heuristic algorithms using this condition to build a schedule belonging to this subset. We also prove dominance theorem, and develop a lower bound that can be computed in polynomial time. We construct a branch-and-bound algorithm in which the heuristic, the lower bound and the dominance properties are incorporated. Computational experiments suggest that the algorithm can handle test problems with 40 jobs and 2 machines.

Generalized g-quasivariational inequality

Suppose that X is a nonempty subset of a metric space E and Y is a nonempty subset of a topological vector space F. Let g:X→Y and ψ:X×Y→ℝ be two functions and let S:X→2Y and T:Y→2F∗ be two maps. Then the generalized g-quasivariational inequality problem (GgQVI) is to find a point x¯∈X and a point f∈T(g(x¯)) such that g(x¯)∈S(x¯) and supy∈S(x¯){Reu2061〈f,y−g(x¯)〉

1. Les enjeux du paradoxe du vote

Les mauvais politiciens sont elus par les bons citoyens qui ne votent pas.George Jean Nathan Presentation Les sens donnes a la participation electorale Les definitions generalement offertes de la democratie insistent souvent sur le caractere central de la participation des citoyens aux elections, au point de faire du vote la cle de voute des regimes democratiques. Nombreux sont les auteurs a defendre ce point de vue, a l’image de Curtis Gans (1978, p. 54) pour qui «xa0la legitimite de la democr...

2. La minimisation du regret maximal

Je n’ai jamais vote pour quelqu’un, j’ai toujours vote contre [quelqu’un].W. C. Fields En cherchant a resoudre le «xa0paradoxe du votexa0», John Ferejohn et Morris Fiorina (1974) ont etabli une distinction interessante entre leur approche et celle d’Anthony Downs (1957). Rappelons que la decision de vote dans le modele de Downs correspond a une decision d’investissementxa0: face a un benefice futur incertain (PB), l’individu se doit de supporter un cout au montant certain (egal a C). Ces auteurs co...

An exact method for Pmsds/,ri/∑i=1nCi problem

This paper addresses an identical parallel machine scheduling problem, with sequence-dependent setup times and release dates to minimize total completion time. This problem is known to be strongly NP-hard. We prove a sufficient and necessary condition for local optimality which can also be considered as a priority rule. We then define a dominant subset based on this condition. We present efficient heuristic algorithms using this condition to build a schedule belonging to this subset. We also prove dominance theorem, and develop a lower bound that can be computed in polynomial time. We construct a branch-and-bound algorithm in which the heuristic, the lower bound and the dominance properties are incorporated. Computational experiments suggest that the algorithm can handle test problems with 40 jobs and 2 machines.