Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics

Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. While very many interesting results have been obtained with this equation in the three decades elapsed since it was first proposed, it is important to realize the limits of its applicability. One particularly relevant issue in this respect is that of non-mean-field effects, that may arise from temporal fluctuations or from spatial correlations, both neglected in the replicator equation. This review discusses these temporal and spatial effects focusing on the non-trivial modifications they induce when compared to the outcome of replicator dynamics. Alongside this question, the hypothesis of linearity and its relation to the choice of the rule for strategy update is also analyzed. The discussion is presented in terms of the emergence of cooperation, as one of the current key problems in Biology and in other disciplines.Comment: Review, 48 pages, 26 figure

Rewarding cooperation in social dilemmas

One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma. Thus, individuals confront a new dilemma: on the one hand, they may be inclined to choose the shared reward despite the possibility of being exploited by defectors; on the other hand, if too many players do that, cooperators will obtain a poor reward and defectors will outperform them. By appropriately tuning the amount to be shared we can cast a vast variety of scenarios, including traditional ones in the study of cooperation as well as more complex situations where unexpected behavior can occur. We provide a complete classification of the equilibria of the nplayer game as well as of the evolutionary dynamics. Beyond, we extend our analysis to a general class of public good games where competition among individuals with the same strategy exists

Time Scales in Evolutionary Dynamics

Evolutionary game theory has traditionally assumed that all individuals in a population interact with each other between reproduction events. We show that eliminating this restriction by explicitly considering the time scales of interaction and selection leads to dramatic changes in the outcome of evolution. Examples include the selection of the inefficient strategy in the Harmony and Stag-Hunt games, and the disappearance of the coexistence state in the Snowdrift game. Our results hold for any population size and in the presence of a background of fitness.Comment: Final version with minor changes, accepted for publication in Physical Review Letter

Assessing the impact of different nominal anchors on the credibility of stabilisation programmes

The paper compares the impact of announcing exchange-rate-based versus money-based stabilisation programmes in a cross-section of countries. The analysis finds that the effect of announcing exchange-rate-based programmes is more credible, in terms of reducing inflation inertia, than the outcome associated with implementing money-based programmes. But the gap between the magnitudes of the impacts from implementing the different strategies has been falling since the 1970s.Inflation stabilisation; credibility; nominal anchors; IMF programmes

Coupled electric and magnetic dipole formulation for planar arrays of dipolar particles: metasurfaces with various electric and/or magnetic meta-atoms per unit cell

The optical properties of infinite planar array of scattering particles, metasurfaces and metagratings, are attracting special attention lately for their rich phenomenology, including both plasmonic and high-refractive-index dielectric meta-atoms with a variety of electric and magnetic resonant responses. Herein we derive a coupled electric and magnetic dipole (CEMD) analytical formulation to describe the reflection and transmission of such periodic arrays, including specular and diffractive orders, valid in the spectral regimes where only dipolar multipoles are needed. Electric and/or magnetic dipoles with all three orientations arising in turn from a single or various meta-atoms per unit cell are considered. The 2D lattice Green function is rewritten in terms of a 1D (chain) version that fully converges and can be easily calculated. Modes emerging as poles of such lattice Green function can be extracted. This formulation can be applied to investigate a wealth of plasmonic, all-dielectric, and hybrid metasurfaces/metagratings of interest throughout the electromagnetic spectrum.Comment: 8 pages, 4 figure

Efficient synthesis of single-chain polymer nanoparticles via amide formation

This is an open access article distributed under the Creative Commons Attribution License.Single-chain technology (SCT) allows the transformation of individual polymer chains to folded/collapsed unimolecular soft nanoparticles. In this work we contribute to the enlargement of the SCT toolbox by demonstrating the efficient synthesis of single-chain polymer nanoparticles (SCNPs) via intrachain amide formation. In particular, we exploit cross-linking between active methylene groups and isocyanate moieties as powerful >click> chemistry driving force for SCNP construction. By employing poly(methyl methacrylate)- (PMMA-) based copolymers bearing β-ketoester units distributed randomly along the copolymer chains and bifunctional isocyanate cross-linkers, SCNPs were successfully synthesized at r.t. under appropriate reaction conditions. Characterization of the resulting SCNPs was carried out by means of a combination of techniques including size exclusion chromatography (SEC), infrared (IR) spectroscopy, proton nuclear magnetic resonance (1H NMR) spectroscopy, dynamic light scattering (DLS), and elemental analysis (EA).Financial support from Projects MAT2012-31088 (MINECO), T-654-13 (GV), and S-PE13UN034 (GV) is acknowledged. Ana Sanchez-Sanchez thanks the Ph.D. grant support of Basque Government.Peer Reviewe

Degenerate optical memory effect in dielectric films with randomly rough surfaces

9 págs.; 6 figs.By means of perturbation theory we calculate the angular intensity correlations of linearly polarized electromagnetic waves scattered from a thin dielectric film deposited on a planar perfectly conducting substrate. The illuminated surface is a one-dimensional, randomly rough surface with a power spectrum given either by a Gaussian, or by a rectangle defined to enhance the coupling into guided waves. The dielectric film supports, at least, two guided waves in the absence of the roughness that have distinct wave numbers at the frequency ω of the incident wave. We analyze the angular dependence of the optical memory effect: In addition to its two well known peaks, we demonstrate that, due to degeneracy of the excitation of guided waves, there appear two pairs of peaks symmetrically located about the former absolute maxima at positions related to the difference between the guided wave numbers. This degenerate memory effect is shown to be a multiple scattering effect. ©1997 American Physical SocietyThis work was supported by the Consejo Superior de Investigaciones Científicas and the Dirección General de Investigación Científica y Técnica through Grant No. PB93- 0973-C02-02.Peer Reviewe

The second Feng-Rao number for codes coming from telescopic semigroups

In this manuscript we show that the second Feng-Rao number of any telescopic numerical semigroup agrees with the multiplicity of the semigroup. To achieve this result we first study the behavior of Ap\'ery sets under gluings of numerical semigroups. These results provide a bound for the second Hamming weight of one-point Algebraic Geometry codes, which improves upon other estimates such as the Griesmer Order Bound