Common use of P&I Clause in Contracts

P&I. Each country in Pi punishes a unilateral deviation by country i by choosing the abatement level qp = pb/c in the period immediately following country i’s deviation, where p ≥ 0. The other signatories including country i (i.e., the countries in M\Pi) ▇▇▇▇▇ at the agreed upon level qs. In the subsequent periods all signatories return to the agreed upon level qs. All non-signatories (i.e, j ∈ N\M ) continue to play their best response q1 throughout. Hence, the punishment path of country i ∈ M is: s = (qp, . . . , qp, qs, . . . , qs, q1, . . . , q1), ` j˛∈¸Pi x ` j∈M˛¸\Pi x ` j∈N˛¸\M x (qs, . . . , qs, q1, . . . , q1), (qs, . . . , qs, q1, . . . , q1), . . . . ` j˛∈¸M x ` j∈N˛¸\M x ` j˛∈¸M x ` j∈N˛¸\M x Since each non-signatory is playing a best response of the stage game, a deviation from the agreement by a non-signatory requires no punish- ment. Hence, even if a non-signatory unilaterally deviates from as or ps for some i ∈ M , the path in question is simply continued, meaning that any such unilateral deviation is followed by as. Hence, formally, the punishment path of country i ∈ N\M equals as. The simple strategy profile determined by the n + 1 paths (as, ps , . . . , ps , as, . . . , as) (4) i1 im ` j∈N˛¸\M x corresponds to what ▇▇▇▇▇ and ▇▇▇▇ (2008) refer to as “Penance k” . In Theorem 1 we establish under what conditions this strategy profile is a weakly renegotiation-proof equilibrium. Since the identities of the signatories and the punishing countries do not matter, as all countries are identical, the conditions of Theorem

P&I. Each country in Pi punishes a unilateral deviation by country i by choosing the abatement level qp = pb/c in the period immediately following country i’s deviation, where p ≥ 0. The other signatories including country i (i.e., the countries in M\Pi) ▇▇▇▇▇ at the agreed upon level qs. In the subsequent periods all signatories return to the agreed upon level qs. All non-signatories (i.e, j ∈ N\M ) continue to play their best response q1 throughout. Hence, the punishment path of country i ∈ M is: s = (qp, . . . , qp, qs, . . . , qs, q1, . . . , q1), ` j˛∈¸Pi x ` j∈M˛¸\Pi x ` j∈N˛¸\M x (qs, . . . , qs, q1, . . . , q1), (qs, . . . , qs, q1, . . . , q1), . . . . ` j˛∈¸M x ` j∈N˛¸\M x ` j˛∈¸M x ` j∈N˛¸\M x Since each non-signatory is playing a best response of the stage game, a deviation from the agreement by a non-signatory requires no punish- ment. Hence, even if a non-signatory unilaterally deviates from as or ps for some i ∈ M , the path in question is simply continued, meaning that any such unilateral deviation is followed by as. Hence, formally, the punishment path of country i ∈ N\M equals as. The simple strategy profile determined by the n + 1 paths (as, ps , . . . , ps , as, . . . , as) (4) i1 im ` j∈N˛¸\M x corresponds to what ▇▇▇▇▇ Froyn and ▇▇▇▇ Hovi (2008) refer to as “Penance k” . In Theorem 1 we establish under what conditions this strategy profile is a weakly renegotiation-proof equilibrium. Since the identities of the signatories and the punishing countries do not matter, as all countries are identical, the conditions of Theorem