  We propose a finite automaton-style solution concept for supergames. In our
model, we define an equilibrium to be a cycle of state switches and a supergame
to be an infinite walk on states of a finite stage game. We show that if the
stage game is locally non-cooperative, and the utility function is monotonously
decreasing as the number of defective agents increases, the symmetric
multiagent prisoners' dilemma supergame must contain one symmetric equilibrium
and can contain asymmetric equilibria.
