  We study the traveling wave solutions to a reaction diffusion system modeling
the public goods game with altruistic behaviors. The existence of the waves is
derived through monotone iteration of a pair of classical upper- and lower
solutions. The waves are shown to be unique and strictly monotonic. A similar
KPP wave like asymptotic behaviors are obtained by comparison principle and
exponential dichotomy. The stability of the traveling waves with non-critical
speed is investigate by spectral analysis in the weighted Banach spaces.
