We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, encompassing the top cycle, the uncovered set, the Banks set, the minimal covering set, and the tournament equilibrium set. Moreover, the hi...

We construct a theory for maximal viscosity solutions of the Cauchy problem for the modiied porous medium equation u t + ju t j = (u m), with 2 (?1; 1) and m > 1. We investigate the existence, uniqueness, nite propagation and optimal regularity of these solutions. As a second main theme we prove that the asymptotic behaviour is given by a certain family of self-similar solutions of the so-calle...

This paper is concerned with the question of defining the bargaining set, a cooperative game solution, when cooperation takes place in a dynamic setting. The focus is on dynamic cooperative games in which the players face (finite or infinite) sequences of exogenously specified TU-games and receive sequences of imputations against those static cooperative games in each time period. Two alternati...

The use of semidefinite programming in combinatorial optimization continues to grow. This growth can be attributed to at least three factors: new semidefinite relaxations that provide tractable bounds to hard combinatorial problems, algorithmic advances in the solution of semidefinite programs (SDP), and the emergence of parallel computing. Solution techniques for minimizing combinatorial probl...

Most, if not all, animals are highly responsive organisms that are capable of adjusting their behaviour during the course of their interactions with others [1]. This observation may seem obvious, yet evolutionary theory has traditionally modelled cooperation and conflict as a ‘sealed bid’, assuming that both parties decide on a fixed strategy without any knowledge of the other’s behaviour [2]. ...

This paper considers a large population randomly matched to play a game of common interest with cheap-talk. We apply a noncooperative solution concept to this society. A strategy distribution g is accessible from another distribution f if there is a path from f to g the direction of which is always a best response to the present distribution. A cyclically stable set is a set of strategy distrib...

Using stable isotope tracers to identify hydrological flow paths, residence times and landscape controls in a mesoscale catchment P. Rodgers , C. Soulsby, S. Waldron, and D. Tetzlaff Department of Geography and Environment, University of Aberdeen, Elphinstone Road, Aberdeen, AB24 3UF, United Kingdom Scottish Universities Environmental Research Centre, Scottish Enterprise Technology Park, East K...

The Pareto stability is one of solution concepts in two-sided matching markets with ties. It is known that there always exists a Pareto stable matching in the many-to-many setting. In this paper, we consider the following generalization of the Pareto stable matching problem in the many-to-many setting. Each agent v of one side has a matroid defined on the set of edges incident to v, and the set...