# Session 2: The Enforcement Game Scott Barrett Johns Hopkins University School of Advanced International Studies.

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Session 2: The Enforcement Game Scott Barrett Johns Hopkins University School of Advanced International Studies

Enforcement Two ways not to cooperate: –Don’t participate; –Participate but don’t comply. Participation and compliance both require enforcement.

Prisoners’ Dilemma…again Y X Could cooperation be enforced if the game were repeated?

Repetition If the game were repeated once, would it be possible to sustain cooperation? Backward induction suggests that the PD must be repeated infinitely often. Alternatively, there must always exist a positive probability that the players will meet again in the future.

Grim Strategy Play Abate in the initial round. Thereafter play Abate provided that neither player has played Pollute in the past; otherwise play Pollute. Two player game: –If the other guy plays Grim, you get a payoff of 1 every period of you play Grim, too. –If you cheat, you get 2 in the current period and 0 every period thereafter.

Nash Equilibrium Better to play Grim if: 1δ 0 +1δ 1 + 1δ 2 + … ≥ 2δ 0 + 0δ 1 + 0δ 2 +… or 1 + δ 1 + δ 2 + … ≥ 2 + 0 + 0 +… or δ 1 + δ 2 + δ 3 +… ≥ 1. This is the same as In other words, play Grim is a NE if r ≤ 100%!

Credibility If you cheat, will the other guy really play Grim? Is the threat to punish indefinitely credible? If you cheat and revert to Grim, you will play Pollute every period after you cheat. So the other guy really can’t do better than to play Grim. The threat is credible—in the sense of being subgame perfect.

Collective Rationality But, hold on. If you both play Grim after either one of you cheats, you are both worse off. Collectively, playing Grim makes no sense. Grim is too unforgiving. It is therefore vulnerable to renegotiation. That is, it is not collectively rational.

Getting-Even Play Abate initially. Thereafter play Abate unless you have played Pollute less often than the other guy in the past. In this case, play Pollute. Example: Suppose other guy plays A A A P A A A…. Then, if you play Getting-Even, you play A A A A P A A… In round 5, you can’t do better than to carry out the punishment Getting-Even promises; so there is no incentive to renegotiate.

N-Player PD The N-Player linear PD has payoffs: with bN > c > b > 0 and q  {0,1}. Provided the players are very patient, it is easy to show that full cooperation can be sustained as a subgame perfect equilibrium for any N (“folk theorem”).

N-Player PD (cont’d) But is a treaty requiring that the cooperating countries play Getting-Even collectively rational? In a punishment phase, if the other countries play Getting-Even, they get a payoff of b every period. If they revert to cooperation, they each get bk – c. Hence better to play Getting-Even if b ≥ bk – c or This is the same condition we obtained previously for the participation stage game.

IR Debate on Compliance Chayes and Chayes: Compliance is not a problem; sticks are not needed. Downs, Rocke, and Barsoom: Compliance is a problem; it only appears not to be a problem because treaties are weak; if compliance could be enforced by sticks, deeper cooperation could be sustained. Barrett: Need to consider compliance and participation jointly. Need sticks to enforce compliance but participation is the binding constraint on cooperation.

International Law Custom says that states must comply with the treaties they sign up to. Compliance asks states to cooperate but it does not require that they participate. So, if you think you won’t comply, better to withdraw—or not participate from the start. Pressure is in the direction of negotiating weak agreements like Helsinki.

Consensus Treaties If we weaken the equilibrium concept (WCR v. SCR), (limited) cooperation can be sustained by any number of players, including N. Fix N and solve for the maximum payoff that can be sustained by a treaty.

Consensus Treaties Suppose j cheats. In a punishment phase, if the other cooperating countries play q j m each, the best payoff j can get is b(N-1)q j m. Hence, given that j has cheated, j will want to re-establish cooperation provided Under the WCR assumption, the other countries will want to punish j by playing q j m in the punishment phase provided

Consensus Treaties A little algebra shows that this implies, This is the maximum payoff that can be sustained by a (WCR) consensus treaty. Credibility v. fairness.

Broad but shallow v. narrow but deep It can be shown that countries will prefer a consensus treaty to an “incomplete, focal” treaty provided In our earlier example, c = 7.5, and b = 1, so c 2 /b 2 = 56.25. If N = 100 (as assumed before), countries would prefer a consensus treaty. If N = 50, however, countries would more likely negotiate a treaty comprising k* = 8 parties.

Fur Seal Compliance Any deviation could trigger a dissolution of the agreement. But “remedial” measures could compensate for non-compliance. Deviations are policed by all parties; compliance is enforced by domestic law. Cash payments took sealing schooners out of service (making enforcement fair). Violations were never recorded.

Montreal Compliance 1987 treaty did not specify punishments for non-compliance. After break up of USSR, Russia indicated that it would not comply. Parties drew up a list of measures to enforce compliance, including assistance (carrots) and penalties (sticks).

Montreal Compliance (cont’d) Other parties offered Russia financial assistance for implementing a post-1996 phase-out, and forbid exports to Article 5 countries. If Russia accepted, it would get assistance. If Russia rejected, it would probably have been subject to trade restrictions at least as great. After making a fuss, Russia accepted the offer.

Kyoto Protocol Climate change mitigation, like ozone layer protection, is a global public good. Kyoto is styled after Montreal. But climate and ozone are different problems; they require different solutions.

Kyoto basics Sets emission limits 2008-2012 for Annex I countries only. Allows trading and JI. Clean development mechanism. Enters into force after being ratified by at least 55 countries making up at least 55% of Annex I CO 2 emissions.

Kyoto will probably enter into force… As of today, 104 countries have ratified, making up 43.9% of Annex I emissions. …but may not have any effect. “Hot air.” Concessions for Japan, Canada, and Russia. Non-compliance is likely (Canada?)

Kyoto enforcement is weak Penalty of 1.3 added in Bonn, but: –Defers punishment. –Future emission limits endogenous. –Relies entirely on self-punishment. –Article 18 requires that “procedures and mechanisms…entailing binding consequences…be adopted by means of an amendment.”

Reasons for Kyoto’s Failure (?) Climate change mitigation has a less favorable cost-benefit ratio. According to Nordhaus & Boyer (2000), the C-B ratio for an optimal climate policy is 3.02. In contrast to the MP, few countries have an incentive to do much unilaterally.

Summary so far Compliance can be made endogenous in a repeated game. Participation and compliance both need to be enforced but participation is the binding constraint on cooperation. Under a weaker notion of collective rationality, there may be a trade-off between the depth and breadth of cooperation.

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