84,508 research outputs found
Heterogeneity in evolutionary games: an analysis of the risk perception
In this work, we analyse the relationship between heterogeneity and
cooperation. Previous investigations suggest that this relation is nontrivial,
as some authors found that heterogeneity sustains cooperation, while others
obtained different results. Among the possible forms of heterogeneity, we focus
on the individual perception of risks and rewards related to a generic event,
that can show up in a number of social and biological systems. The modelling
approach is based on the framework of Evolutionary Game Theory. To represent
this kind of heterogeneity, we implement small and local perturbations on the
payoff matrix of simple 2-strategy games, as the Prisoner's Dilemma. So, while
usually the payoff is considered as a global and time-invariant structure, i.e.
it is the same for all individuals of a population at any time, in our model
its value is continuously affected by small variations, both in time and space
(i.e. position on a lattice). We found that such perturbations can be
beneficial or detrimental to cooperation, depending on their setting. Notably,
cooperation is strongly supported when perturbations act on the main diagonal
of the payoff matrix, whereas when they act on the off-diagonal the resulting
effect is more difficult to quantify. To conclude, the proposed model shows a
rich spectrum of possible equilibria, whose interpretation might offer insights
and enrich the description of several systems.Comment: 7 pages, 5 figure
A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems
We introduce a derivative-free computational framework for approximating
solutions to nonlinear PDE-constrained inverse problems. The aim is to merge
ideas from iterative regularization with ensemble Kalman methods from Bayesian
inference to develop a derivative-free stable method easy to implement in
applications where the PDE (forward) model is only accessible as a black box.
The method can be derived as an approximation of the regularizing
Levenberg-Marquardt (LM) scheme [14] in which the derivative of the forward
operator and its adjoint are replaced with empirical covariances from an
ensemble of elements from the admissible space of solutions. The resulting
ensemble method consists of an update formula that is applied to each ensemble
member and that has a regularization parameter selected in a similar fashion to
the one in the LM scheme. Moreover, an early termination of the scheme is
proposed according to a discrepancy principle-type of criterion. The proposed
method can be also viewed as a regularizing version of standard Kalman
approaches which are often unstable unless ad-hoc fixes, such as covariance
localization, are implemented. We provide a numerical investigation of the
conditions under which the proposed method inherits the regularizing properties
of the LM scheme of [14]. More concretely, we study the effect of ensemble
size, number of measurements, selection of initial ensemble and tunable
parameters on the performance of the method. The numerical investigation is
carried out with synthetic experiments on two model inverse problems: (i)
identification of conductivity on a Darcy flow model and (ii) electrical
impedance tomography with the complete electrode model. We further demonstrate
the potential application of the method in solving shape identification
problems by means of a level-set approach for the parameterization of unknown
geometries
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