Deflated GMRES for Systems with Multiple Shifts and Multiple Right-Hand Sides

We consider solution of multiply shifted systems of nonsymmetric linear equations, possibly also with multiple right-hand sides. First, for a single right-hand side, the matrix is shifted by several multiples of the identity. Such problems arise in a number of applications, including lattice quantum chromodynamics where the matrices are complex and non-Hermitian. Some Krylov iterative methods such as GMRES and BiCGStab have been used to solve multiply shifted systems for about the cost of solving just one system. Restarted GMRES can be improved by deflating eigenvalues for matrices that have a few small eigenvalues. We show that a particular deflated method, GMRES-DR, can be applied to multiply shifted systems. In quantum chromodynamics, it is common to have multiple right-hand sides with multiple shifts for each right-hand side. We develop a method that efficiently solves the multiple right-hand sides by using a deflated version of GMRES and yet keeps costs for all of the multiply shifted systems close to those for one shift. An example is given showing this can be extremely effective with a quantum chromodynamics matrix.Comment: 19 pages, 9 figure

Altruistic Behavior and Correlated Equilibrium Selection

This paper studies new refinement concepts for correlated equilibria based on altruistic behavior of the players and which generalize some refinement concepts introduced by the authors in previous papers for Nash equilibria. Effectiveness of the concepts, relations with the corresponding notions for Nash equilibria and with other correlated equilibrium refinements are investigated. The analysis of the topological properties of the set of solutions concludes the paper.correlated equilibrium, altruistic behavior, refinement

Kalai-Smorodinsky Bargaining Solution Equilibria

Multicriteria games describe strategic interactions in which players, having more than one criterion to take into account, don't have an a-priori opinion on the rel- ative importance of all these criteria. Roemer (2005) introduces an organizational interpretation of the concept of equilibrium: each player can be viewed as running a bargaining game among criteria. In this paper, we analyze the bargaining problem within each player by considering the Kalai-Smorodinsky bargaining solution. We provide existence results for the so called Kalai-Smorodinsky bargaining solution equilibria for a general class of disagreement points which properly includes the one considered in Roemer (2005). Moreover we look at the refinement power of this equilibrium concept and show that it is an effective selection device even when combined with classical refinement concepts based on stability with respect to perturbations such as the the extension to multicriteria games of the Selten's (1975) trembling hand perfect equilibrium concept.

Slightly Altruistic Equilibria in Normal Form Games

We introduce a refinement concept for Nash equilibria (slightly altruistic equilibrium) defined by a limit process and which captures the idea of reciprocal altruism as presented in Binmore (2003). Existence is guaranteed for every finite game and for a large class of games with a continuum of strategies. Results and examples emphasize the (lack of) connections with classical refinement concepts. Finally, it is shown that under a pseudo-monotonicity assumption on a particular operator associated to the game it is possible, by selecting slightly altruistic equilibria, to eliminate those equilibria in which a player can switch to a strategy that is better for the others without leaving the set of equilibria.

On Multicriteria Games with Uncountable Sets of Equilibria

The famous Harsanyi's (1973) Theorem states that generically a finite game has an odd number of Nash equilibria in mixed strategies. In this paper, we show that for finite multicriteria games (games with vector-valued payoffs) this kind of result does not hold. In particular, we show, by examples, that it is possible to find balls in the space of games such that every game in this set has uncountably many equilibria so that uncountable sets of equilibria are not nongeneric in multicriteria games. Moreover, we point out that, surprisingly, all the equilibria of the games cor- responding to the center of these balls are essential, that is, they are stable with respect to every possible perturbation on the data of the game. However, if we consider the scalarization stable equilibrium concept (introduced in De Marco and Morgan (2007) and which is based on the scalarization technique for multicriteria games), then we show that it provides an effective selection device for the equilibria of the games corresponding to the centers of the balls. This means that the scalarization stable equilibrium concept can provide a sharper selection device with respect to the other classical refinement concepts in multicriteria games.

Social Networks: Equilibrium Selection and Friendliness

Given their importance in determining the outcome of many economic interactions, different models have been proposed to determine how social networks form and which structures are stable. In Bala and Goyal (2000), the one-sided link formation model has been considered, which is based on a noncooperative game of network formation. They found out that the empty networks, the wheel in the one-way flow of benefits case and the center sponsored star in the two-way flow case play a fundamental role, since they are strict Nash equilibria of the corresponding games for certain classes of payoff functions. In this paper, firstly we prove that all these network structures are in weakly dominated strategies whenever there are no strict Nash equilibria. Then, we exhibit a more accurate selection device between these network architectures by considering ‘altruistic behavior’ refinements. Such refinements, that we investigate here in the framework of finite strategy sets games, have been introduced by the authors in previous papers.

First-principles study of magnetism in spinel MnO2

First-principles electronic structure methods have been used to calculate the ground state, transition temperature, and thermodynamic properties of magnetic excitations in spinel MnO2. The magnetic interactions are mapped onto a Heisenberg model whose exchange interactions are fitted to results of first-principles calculations of different spin configurations. The thermodynamics are calculated using Monte Carlo methods. The Heisenberg model gives an extremely accurate representation of the true first-principles magnetic energies. We find a critical temperature and Weiss constant significantly larger than experimental results and believe the error to come from the local spin density approximation. We predict a new magnetic ground state different from that proposed previously, but consistent with experimental data

Participatory approach for integrated basin planning with focus on disaster risk reduction : the case of the Limpopo river

This paper defends the idea that a participatory approach is a suitable method for basin planning integrating both water and land aspects. Assertions made are based on scientific literature review and corroborated by field experience and research carried out in the Limpopo River basin, a transboundary river located in southern Africa which is affected by periodical floods. The paper explains how a basin strategic plan can be drafted and disaster risk reduction strategies derived by combining different types of activities using a bottom-up approach, despite an institutional context which operates through traditional top-down mechanisms. In particular, the "Living with Floods" experience in the lower Limpopo River, in Mozambique, is described as a concrete example of a disaster adaptation measure resulting from a participatory planning exercise. In conclusion, the adopted method and obtained results are discussed and recommendations are formulated for potential replication in similar contexts of the developing world