HedN Game, a Relational Framework for Network Based Cooperation

This paper proposes a new framework for cooperative games based on mathematical relations. Here cooperation is defined as a supportive partnerships represented by a directed network between players (aka hedonic relation). We examine in a specific context, modeled by abstract games how a change of supports induces a modification of strategic interactions between players. Two levels of description are considered: the first one describes the support network formation whereas the second one models the strategic interactions between players. Both are described in a unified formalism, namely CP~game. Stability conditions are stated, emphasizing the connection between these two levels. We also stress the interaction between updates of supports and their impact on the evolution of the context.Cooperative Game, Network, Stability, Hedonic Relation

The Community Structure of R&D Cooperation in Europe. Evidence from a social network perspective

The focus of this paper is on pre-competitive R&D cooperation across Europe, as captured by R&D joint ventures funded by the European Commission in the time period 1998-2002, within the 5th Framework Program. The cooperations in this Framework Program give rise to a bipartite network with 72,745 network edges between 25,839 actors (representing organizations that include firms, universities, research organizations and public agencies) and 9,490 R&D projects. With this construction, participating actors are linked only through joint projects. In this paper we describe the community identification problem based on the concept of modularity, and use the recently introduced label-propagation algorithm to identify communities in the network, and differentiate the identified communities by developing community-specific profiles using social network analysis and geographic visualization techniques. We expect the results to enrich our picture of the European Research Area by providing new insights into the global and local structures of R&D cooperation across Europe

A tale of three homotopies

For a Koszul operad $\mathcal{P}$, there are several existing approaches to the notion of a homotopy between homotopy morphisms of homotopy $\mathcal{P}$-algebras. Some of those approaches are known to give rise to the same notions. We exhibit the missing links between those notions, thus putting them all into the same framework. The main nontrivial ingredient in establishing this relationship is the homotopy transfer theorem for homotopy cooperads due to Drummond-Cole and Vallette.Comment: 22 pages, final versio

On Hopf algebra structures over free operads

The operad Lie can be constructed as the operad of primitives Prim As from the operad As of associative algebras. This is reflected by the theorems of Friedrichs, Poincare'-Birkhoff-Witt and Cartier-Milnor-Moore. We replace As by families of free operads P, which include the operad Mag freely generated by a noncommutative non-associative binary operation and the operad of Stasheff polytopes. We obtain Poincare'-Birkhoff-Witt type theorems and collect information about the operads Prim P, e.g. in terms of characteristic functions.Comment: 25pages, uses elsart.cls, paper extracted from habilitation thesis (math.RA/0407074), revised (more details in sections 2,3,4, and 6