  Populations composed of a collection of subpopulations (demes) with random
migration between them are quite common occurrences. The emergence and
sustenance of cooperation in such a population is a highly researched topic in
the evolutionary game theory. If the individuals in every deme are considered
to be either cooperators or defectors, the migration dilemma can be envisaged:
The cooperators would not want to migrate to a defector-rich deme as they fear
of facing exploitation; but without migration, cooperation can not be
established throughout the network of demes. With a view to studying the
aforementioned scenario, in this paper, we set up a theoretical model
consisting of a coupled map lattice of replicator maps based on
two-player--two-strategy games. The replicator map considered is capable of
showing a variety of evolutionary outcomes, like convergent (fixed point)
outcomes and nonconvergent (periodic and chaotic) outcomes. Furthermore, this
coupled network of the replicator maps undergoes the phenomenon of amplitude
death leading to non-oscillatory stable synchronized states. We specifically
explore the effect of (i) the nature of coupling that models migration between
the maps, (ii) the heterogenous demes (in the sense that not all the demes have
same game being played by the individuals), (iii) the degree of the network,
and (iv) the cost associated with the migration. In the course of
investigation, we are intrigued by the effectiveness of the random migration in
sustaining a uniform cooperator fraction across a population irrespective of
the details of the replicator dynamics and the interaction among the demes.
