A spatial model for selection and cooperation

We study the evolution of cooperation in an interacting particle system with two types. The model we investigate is an extension of a two-type biased voter model. One type (called defector) has a (positive) bias $\alpha$ with respect to the other type (called cooperator). However, a cooperator helps a neighbor (either defector or cooperator) to reproduce at rate $\gamma$. We prove that the one-dimensional nearest-neighbor interacting dynamical system exhibits a phase transition at $\alpha=\gamma$. For $\alpha>\gamma$ cooperators always die out, but if $\gamma>\alpha$, cooperation is the winning strategy.Comment: 19 pages, 1 figur

Two axiomatizations of the kernel of TU games: bilateral and converse reduced game properties

We provide two axiomatic characterizations of the kernel of TU games by means of both bilateral consistency and converse consistency with respect to two types of two-person reduced games. According to the first type, the worth of any single player in the two-person reduced game is derived from the difference of player's positive (instead of maximum) surpluses. According to the second type, the worth of any single player in the two-person reduced game either coincides with the two-person max reduced game or refers to the constrained equal loss rule applied to an appropriate two-person bankruptcy problem, the claims of which are given by the player's positve surpluses

Cooperative heterogeneous facilitation: multiple glassy states and glass-glass transition

The formal structure of glass singularities in the mode-coupling theory (MCT) of supercooled liquids dynamics is closely related to that appearing in the analysis of heterogeneous bootstrap percolation on Bethe lattices, random graphs and complex networks. Starting from this observation one can build up microscopic on lattice realizations of schematic MCT based on cooperative facilitated spin mixtures. I discuss a microscopic implementation of the F13 schematic model including multiple glassy states and the glass-glass transition. Results suggest that our approach is flexible enough to bridge alternative theoretical descriptions of glassy matter based on the notions of quenched disorder and dynamic facilitation.Comment: 4 pages, 2 figure

Percolation approach to glassy dynamics with continuously broken ergodicity

We show that the relaxation dynamics near a glass transition with continuous ergodicity breaking can be endowed with a geometric interpretation based on percolation theory. At mean-field level this approach is consistent with the mode-coupling theory (MCT) of type-A liquid-glass transitions and allows to disentangle the universal and nonuniversal contributions to MCT relaxation exponents. Scaling predictions for the time correlation function are successfully tested in the F12 schematic model and facilitated spin systems on a Bethe lattice. Our approach immediately suggests the extension of MCT scaling laws to finite spatial dimensions and yields new predictions for dynamic relaxation exponents below an upper critical dimension of 6

Coalitionally Monotonic Set-solutions for Cooperative TU Games

A static comparative study on set-solutions for cooperative TU games is carried out. The analysis focuses on studying the compatibility between two classical and reasonable properties introduced by Young (1985) in the context of single valued solutions, namely core-selection and coalitional monotonicity. As the main result, it is showed that coalitional monotonicity is not only incompatible with the core-selection property but also with the bargaining-selection property. This new impossibility result reinforces the trade-off between these kinds of interesting and intuitive economic properties. Positive results about compatibility between desirable economic properties are given replacing the core- selection requirement by the core-extension property.core-extension, bargaining-selection, set-solution, coalitional monotonicity, core-selection