  Infinitely repeated games can support cooperative outcomes that are not
equilibria in the one-shot game. The idea is to make sure that any gains from
deviating will be offset by retaliation in future rounds. However, this model
of cooperation fails in anonymous settings with many strategic agents that
interact in pairs. Here, a player can defect and then avoid penalization by
immediately switching partners. In this paper, we focus on a specific set of
equilibria that avoids this pitfall. In them, agents follow a designated
sequence of actions, and restart if their opponent ever deviates. We show that
the socially-optimal sequence of actions consists of an infinitely repeating
goal value, preceded by a hazing period. We introduce an equivalence relation
on sequences and prove that the computational problem of finding a
representative from the optimal equivalence class is (weakly) NP-hard.
Nevertheless, we present a pseudo-polynomial time dynamic program for this
problem, as well as an integer linear program, and show they are efficient in
practice. Lastly, we introduce a fully polynomial-time approximation scheme
that outputs a hazing sequence with arbitrarily small approximation ratio.
