  Finding ways to overcome the temptation to exploit one another is still a
challenge in behavioural sciences. In the framework of evolutionary game
theory, punishing strategies are frequently used to promote cooperation in
competitive environments. Here, we introduce altruistic punishers in the
spatial public goods game. This strategy acts as a cooperator in the absence of
defectors, otherwise it will punish all defectors in their vicinity while
bearing a cost to do so. We observe three distinct behaviours in our model: i)
in the absence of punishers, cooperators (who don't punish defectors) are
driven to extinction by defectors for most parameter values; ii) clusters of
punishers thrive by sharing the punishment costs when these are low iii) for
higher punishment costs, punishers, when alone, are subject to exploitation but
in the presence of cooperators can form a symbiotic spatial structure that
benefits both. This last observation is our main finding since neither
cooperation nor punishment alone can survive the defector strategy in this
parameter region and the specificity of the symbiotic spatial configuration
shows that lattice topology plays a central role in sustaining cooperation.
Results were obtained by means of Monte Carlo simulations on a square lattice
and subsequently confirmed by a pairwise comparison of different strategies'
payoffs in diverse group compositions, leading to a phase diagram of the
possible states.
