  An evolutionary prisoner's dilemma (PD) game is studied with players located
on a hierarchical structure of layered square lattices. The players can follow
two strategies [D (defector) and C (cooperator)] and their income comes from PD
games with the ``neighbors.'' The adoption of one of the neighboring strategies
is allowed with a probability dependent on the payoff difference. Monte Carlo
simulations are performed to study how the measure of cooperation is affected
by the number of hierarchical levels (Q) and by the temptation to defect.
According to the simulations the highest frequency of cooperation can be
observed at the top level if the number of hierarchical levels is low (Q<4).
For larger Q, however, the highest frequency of cooperators occurs in the
middle layers. The four-level hierarchical structure provides the highest
average (total) income for the whole community.
