  The emergence and promotion of cooperation are two of the main issues in
evolutionary game theory, as cooperation is amenable to exploitation by
defectors, which take advantage of cooperative individuals at no cost, dooming
them to extinction. It has been recently shown that the existence of purely
destructive agents (termed jokers) acting on the common enterprises (public
goods games) can induce stable limit cycles among cooperation, defection, and
destruction when infinite populations are considered. These cycles allow for
time lapses in which cooperators represent a relevant fraction of the
population, providing a mechanism for the emergence of cooperative states in
nature and human societies. Here we study analytically and through agent-based
simulations the dynamics generated by jokers in finite populations for several
selection rules. Cycles appear in all cases studied, thus showing that the
joker dynamics generically yields a robust cyclic behavior not restricted to
infinite populations. We also compute the average time in which the population
consists mostly of just one strategy and compare the results with numerical
simulations.
