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

On string models with Scherk-Schwarz supersymmetry breaking

We construct a general class of chiral four-dimensional string models with Scherk--Schwarz supersymmetry breaking, involving freely acting orbifolds. The basic ingredient is to combine an ordinary supersymmetry-preserving Z_N projection with a supersymmetry-breaking projection Z_M' acting freely on a subspace of the internal manifold. A crucial condition is that any generator of the full orbifold group Z_N x Z_M' must either preserve some supersymmetry or act freely in order to become irrelevant in some large volume limit. Tachyons are found to be absent or limited to a given region of the tree-level moduli space. We find several new models with orthogonal supersymmetries preserved at distinct fixed-points. Particular attention is devoted to an interesting Z_3 x Z_3' heterotic example.Comment: v2: Minor corrections and a reference added; v3: Title and abstract slightly changed, figure 2 corrected and a reference adde