# Journée TADJ

Dans le cadre du projet du groupe de travail THEORIE ALGORITHMIQUE DE LA DECISION ET DES JEUX (TADJ) du GDR RO nous organisons le 28 Novembre 2016 à l’Université Paris Dauphine en salle A709 une matinée de séminaires ouverte à tous.

Voici le programme de la matinée:

- 9h-9h30 : Accueil café-croissant.

- 9h30-10h10 : Roberto Lucchetti (Politecnico di Milano) : "Axiomatization of a value for ternary games".

- 10h10-10h50 : Francesca Fossati (LIP6) : "Mood Value: A Game-Theoretic Fair Resource Allocation Concept".

- 10h50-11h30 : Stefano Moretti (Lamsade) : "On cooperative connection situations where the players are located at the edges".

Résumés des interventions :

**Axiomatization of a value for ternary games**

*Roberto Lucchetti *

Classical theory of simple games does not allow studying voting situations when voters can also abstain and the output is binary, i.e., either approval or rejection. Thus a new model of games, called ternary games, has been recently developed. Also in this context power indices are of great importance. In this context a power index should be a pair of real numbers, since this better highlights the power of a voter in two different cases, i.e., her being crucial when switching from being in favor to abstain, and from abstain to be contrary. We provide an axiomatization for both indices, and from this a characterization of the standard Banzhaf index (which is the sum of the former two) is obtained.

**Mood Value: A Game-Theoretic Fair Resource Allocation Concept**

*Francesca Fossati*

In networking and computing, resource allocation is typically addressed using classical sharing protocols as, for instance, the proportional fairness division, the max-min fairness allocation, or other solutions inspired by cooperative game theory. There are interactive and constrained resource situations for which such classical resource allocation approaches, as well as associated notions of fairness, show important limitations. We identify in the individual satisfaction rate the key aspect of the challenge of defining a new notion of fairness and, consequently, more appropriate resource allocation algorithms. We propose a game-theoretical approach to generalize the concept of user satisfaction considering the set of admissible solutions for bankruptcy games. We adapt the Jain's fairness index to include the new user satisfaction rate. Accordingly, we propose a new allocation rule, we call `Mood

Value', such that it equalizes our novel game-theoretic de notion of user satisfaction with respect to a repartition of the resource.

**On cooperative connection situations where the players are located at the edges**

*Stefano Moretti*

In classical cooperative connection situations, the players are located at some nodes of a network and the cost of a coalition is based on the problem of finding a network of minimum cost connecting all the players in the coalition to a source.

In this paper we study a different connection situation with no source and where the players are the edges, and yet the optimal network associated to each coalition (of edges) is not fixed and follows a cost-optimization procedure. The proposed model shares some similarities with classical minimum cost spanning tree games, but also substantial differences, specifically on the appropriate way to share the costs among the players located at the edges. We show that the core of these particular cooperative games is always non-empty and some core allocations can be easily computed.