  Taxes are an essential and uniformly applied institution for maintaining
modern societies. However, the levels of taxation remain an intensive debate
topic among citizens. If each citizen contributes to common goals, a minimal
tax would be sufficient to cover common expenses. However, this is only
achievable at high cooperation level; hence, a larger tax bracket is required.
A recent study demonstrated that if an appropriate tax partially covers the
punishment of defectors, cooperation can be maintained above a critical level
of the multiplication factor, characterizing the synergistic effect of common
ventures. Motivated by real-life experiences, we revisited this model by
assuming an interactive structure among competitors. All other model elements,
including the key parameters characterizing the cost of punishment, fines, and
tax level, remain unchanged. The aim was to determine how the spatiality of a
population influences the competition of strategies when punishment is partly
based on a uniform tax paid by all participants. This extension results in a
more subtle system behavior in which different ways of coexistence can be
observed, including dynamic pattern formation owing to cyclic dominance among
competing strategies.
