From entangled codipterous coalgebras to coassociative manifolds

We construct from coassociative coalgebras, bialgebras, Hopf algebras, new objects such as Poisson algebras, Leibniz algebras defined by J-L Loday and M. Ronco and explore the notion of coassociative manifolds.Comment: 25 pages, 13 figure

Construction of Nijenhuis operators and dendriform trialgebras

Nijenhuis operators are constructed from particular bialgebras called dendriform- Nijenhuis bialgebras. It turns out that such operators commute with TD-operators, kind of Baxter-Rota operators, and therefore closely related to dendriform trialgebras. Examples are given.Comment: 21 page

On some remarkable operads constructed from Baxter operators

Language theory, symbolic dynamics, modelisation of viral insertion into the genetic code of a host cell motivate the introduction of new types of bialgebras whose coalgebra parts are not necessarily coassociative. One of the aim of this article is to study what type of (associative) algebras (and thus binary quadratic and non-symmetric operads) appear when such or such coalgebraic structures are used to decribe for instance combinatorial objects such as weighted directed graphs, trees, substitutions and so forth.Comment: 45 pages, 4 figure

A discussion of the consistency axiom in cost-allocation problems

The recent literature on cost allocation lacks consensus on what is an appropriate definition of the consistency axiom. We take this as evidence that a careful reexamination is necessary. The starting point of our critique is the widely adopted definition proposed in Moulin and Shenker (1994), which we show to be conceptually flawed. Rectifying this flaw leads to a definition of consistency which already appeared in the recent literature though without satisfactory conceptual justification. We offer a classification of the existing definitions of the consistency axiom by relating them to the definitions of consistency in cooperative games suggested in Davis and Maschler (1965) and Hart and Mas-Colell (1989). We argue that only the latter leads to a meaningful interpretation of consistency when production externalities are present.

Pooling Private Technologies: Improving upon Autarky

When n agents decide to pool their private, decreasing returns technologies, single-path methods are a natural way to share joint output because of their strong incentives properties (Friedman, 2002). They are a non-anonymous generalization of the serial rule (Moulin and Shenker, 1992) sharing a production function along a prespecified path. We show that only one of these methods satisfies voluntary participation; its generating path is entirely determined by the n production functions. This yields a bijection between single-path methods and distributions of property rights on a single technology. Also, we show that these methods are characterized by their incentives properties in the 2-agent case, but not for n >= 3.