This study provides a new framework for international environmental agreements (IEAs), which include punishment exceptions for accidental deviation, using repeated games. We consider that deviation from an agreement can occur accidentally because of phenomena such as natural disasters, even if the agreement is sustained as a weakly renegotiation-proof equilibrium. If an IEA signatory deviates accidentally, it fails to achieve its emission abatement target. In the repeated game, a cooperative relationship among signatories is sustained by a strategy that prescribes rules of cooperation and punishment for deviation. We present a new strategy, called Regional Cooperative, which integrates accidental deviations into an IEA. Our model reveals that punishing countries tend to revoke the punishment of deviators and return to cooperation if an accidental deviator increases its abatement volume. That is, the abatement efforts of the accidental deviator can lead to renegotiation. The Regional Cooperative strategy motivates the accidental deviator to try to engage in abatement and the punishing countries to restart cooperation by renegotiation. We conclude that social welfare loss by punishment is prevented through renegotiation in cases of accidental deviation.
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