  This work deals with the time evolution of the Hamming distance density for
the public goods game. We consider distinct possibilities for this game, which
are exactly described by a function called $q$-exponential, that represents a
deformation of the usual exponential function parametrized by $q$, suggesting
that the system belongs to the class of weakly-chaotic systems when $q < 1$.
These possibilities are related to the amount of players allowed in each game.
