  Maintenance of cooperation was studied for a two-strategy evolutionary
Prisoner's Dilemma game where the players are located on a one-dimensional
chain and their payoff comes from games with the nearest and next-nearest
neighbor interactions. The applied host geometry makes possible to study the
impacts of two conflicting topological features. The evolutionary rule involves
some noise affecting the strategy adoptions between the interacting players.
Using Monte Carlo simulations and the extended versions of dynamical mean-field
theory we determined the phase diagram as a function of noise level and a
payoff parameter. The peculiar feature of the diagram is changed significantly
when the connectivity structure is extended by extra links as suggested by
Newman and Watts.
