too late, so we make sure that Player i is hit really hard for L periods before switching to the conciliation phase Finally, the second condition on d has the following interpretation: by punishing Player j Player i potentially loses M-ui(p-, Ti(p-i))for the L periods following Player j 's deviation (be it a deviation from a(0)or from whatever j was supposed to play). On the other hand after L rounds of punishments, the game will switch to the C() conciliation stage. Now, Player i prefers to be in the C( state than in the C(i) state, by assumption, so if the discount factor is large enough, she will not deviate The only subtle point is that she may actually deviate at any t E 1, .., L)(where time is measured starting from the first stage after Player j's deviation). If she deviates at t, she will actually be held down to vi starting from t+1 and until t+L>L+1; the condition in the text is thus stronger than it needs be(it assumes a payoff of M from t+ l to L, and a punishment payoff of ui(a(i)) from L+l to t+Ltoo late, so we make sure that Player j is hit really hard for L periods before switching to the conciliation phase. Finally, the second condition on δ has the following interpretation: by punishing Player j, Player i potentially loses M −ui(p−j , rj (p−j )) for the L periods following Player j’s deviation (be it a deviation from a(0) or from whatever j was supposed to play). On the other hand, after L rounds of punishments, the game will switch to the C(j) conciliation stage. Now, Player i prefers to be in the C(j) state than in the C(i) state, by assumption, so if the discount factor is large enough, she will not deviate. [The only subtle point is that she may actually deviate at any t ∈ {1, . . . , L} (where time is measured starting from the first stage after Player j’s deviation). If she deviates at t, she will actually be held down to vi starting from t + 1 and until t + L ≥ L + 1; the condition in the text is thus stronger than it needs be (it assumes a payoff of M from t + 1 to L, and a punishment payoff of ui(a(i)) from L + 1 to t + L).] 5