  Population diversity is an important aspect of Prisoner's Dilemma Game (PDG)
research. However, the studies on dynamic diversity and its associated cost
still need further investigation. Based on a framework comprising 2-dimensional
spatial evolutionary PDG, this work examines the change in a player's
neighborhood by enabling each player to pay for an upgrade of their
neighborhood to switch from the von Neumann to Moore neighborhood. The upgrade
cost (i.e., the cost of the advanced neighborhood) plays a vital role in
cooperation promotion and serves as an entry-level to screen players. The
results show that a reasonable price (entry-level) supports the cooperators'
survival in an environment with high dilemma strength since it allows the
formation of "normal-edge-advantage-core" clusters. On the low entry-level
side, the privilege of having a larger neighborhood supports cooperation if it
is accessible to all the players. On the high entry-level side, encirclements
of advantage defectors appear out of the cooperative clusters. To break the
encirclement and enable the expansion of the advantage clusters, the
entry-level should be increased to interrupt the advantage defectors. The
encirclement can be observed only in the deterministic models. Stochastic
simulations are provided as robustness benchmarks.
