The Prisoner’s dilemma is the main game theoretical framework in which the onset and maintainance of cooperation in biological populations is studied. In the spatial version of the model, we study the robustness of cooperation in heterogeneous ecosystems in spatial evolutionary games by considering site diluted lattices. The main result is that, due to disorder, the fraction of cooperators in the population is enhanced. Moreover, the system presents a dynamical transition at ${\rho }^{*},$ separating a region with spatial chaos from one with localized, stable groups of cooperators.

We study the evolution of cooperation in evolutionary spatial games when the payoff correlates with the increasing age of players (the level of correlation is set through a single parameter, $\alpha${}). The demographic heterogeneous age distribution, directly affecting the outcome of the game, is thus shown to be responsible for enhancing the cooperative behavior in the population. In particular, moderate values of $\alpha${} allow cooperators not only to survive but to outcompete defectors, even when the temptation to defect is large and the ageless, standard $\alpha${}=0 model does not sustain cooperation. The interplay between age structure and noise is also considered, and we obtain the conditions for optimal levels of cooperation.

We consider the statistics of the areas enclosed by domain boundaries (“hulls”) during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area that enclose an area greater than $A$ has, for large time $t$, the scaling form $N_h(A,t)=2c/(A+\lambda t)$, demonstrating the validity of dynamical scaling in this system, where $c=1/8\pi \sqrt{3}$ is a universal constant. Domain areas (regions of aligned spins) have a similar distribution up to very large values of $A/\lambda t$. Identical forms are obtained for coarsening from a critical initial state, but with $c$ replaced by $c/2$.

Monte Carlo simulations are used to study lattice gases of particles with extended hard cores on a two-dimensional square lattice. Exclusions of one and up to five nearest neighbors (NN) are considered. These can be mapped onto hard squares of varying side length, $\lambda$ (in lattice units), tilted by some angle with respect to the original lattice. In agreement with earlier studies, the 1NN exclusion undergoes a continuous order-disorder transition in the Ising universality class. Surprisingly, we find that the lattice gas with exclusions of up to second nearest neighbors (2NN) also undergoes a continuous phase transition in the Ising universality class, while the Landau–Lifshitz theory predicts that this transition should be in the universality class of the XY model with cubic anisotropy. The lattice gas of 3NN exclusions is found to undergo a discontinuous order-disorder transition, in agreement with the earlier transfer matrix calculations and the Landau–Lifshitz theory. On the other hand, the gas of 4NN exclusions once again exhibits a continuous phase transition in the Ising universality class—contradicting the predictions of the Landau–Lifshitz theory. Finally, the lattice gas of 5NN exclusions is found to undergo a discontinuous phase transition.