  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.
