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

Altruistic behavior pays, or the importance of fluctuations in evolutionary game theory

Human behavior is one of the main problems for evolution, as it is often the case that human actions are disadvantageous for the self and advantageous for other people. Behind this puzzle are our beliefs about rational behavior, based on game theory. Here we show that by going beyond the standard game-theoretical conventions, apparently altruistic behavior can be understood as self-interested. We discuss in detail an example related to the so called Ultimatum game and illustrate the appearance of altruistic behavior induced by fluctuations. In addition, we claim that in general settings, fluctuations play a very relevant role, and we support this claim by considering a completely different example, namely the Stag-Hunt game.Comment: For the proceedings of the 8th Granada Seminar on Computational Physics (AIP Proceedeings Series

Imperfect Imitation Can Enhance Cooperation

The promotion of cooperation on spatial lattices is an important issue in evolutionary game theory. This effect clearly depends on the update rule: it diminishes with stochastic imitative rules whereas it increases with unconditional imitation. To study the transition between both regimes, we propose a new evolutionary rule, which stochastically combines unconditional imitation with another imitative rule. We find that, surprinsingly, in many social dilemmas this rule yields higher cooperative levels than any of the two original ones. This nontrivial effect occurs because the basic rules induce a separation of timescales in the microscopic processes at cluster interfaces. The result is robust in the space of 2x2 symmetric games, on regular lattices and on scale-free networks.Comment: 4 pages, 4 figure

A new Skyrme interaction with improved spin-isospin properties

A correct determination of the spin-isospin properties of the nuclear effective interaction should lead, among other improvements, to an accurate description of the Gamow-Teller Resonance (GTR). These nuclear excitations impact on a variety of physical processes: from the response in charge-exchange reactions of nuclei naturally present in the Earth, to the description of the stellar nucleosynthesis, and of the pre-supernova explosion core-collapse evolution of massive stars in the Universe. A reliable description of the GTR provides also stringent tests for neutrinoless double-$\beta$ decay calculations. We present a new Skyrme interaction as accurate as previous forces in the description of finite nuclei and of uniform matter properties around saturation density, and that account well for the GTR in ${}^{48}$Ca, ${}^{90}$Zr and ${}^{208}$Pb, the Isobaric Analog Resonance and the Spin Dipole Resonance in ${}^{90}$Zr and ${}^{208}$Pb.Comment: Predictions on the IAR and SDR and comparison with the SGII interaction for the GTRs where adde