1IncentivestojoinaMEANotes in this section are based on Chapters 3 and 6 of Scott Barrett’sEn vironment and Statecraft, Oxfor d Press, 2003.)Many transnational en vironm ental problem s can be described as prisonersdilemma. In this game, the group as a whole — and eac h individual in thegroup — would be better off if all agen ts cooperated. However, each individ ualhas an incentive to "defect" from a cooperativ e agreement. ME A s provideapartialresolutionofthisdilemma,butMEAsmaynotbeabletosustaincom plete cooperation . Agents decide whe ther or not to participate (i.e. tojoin) an MEA ; this decision whether to join the agreement is modelled by a"particip atio n game". The prisoner’s dilemm a game is a building block forthe participation game.By assumption, the MEA is able to reach an agreement that maximizesits members’ join t welfare. The ME A understands that non-members willpursu e their self-in terest, as described b y the prisoner’s dilemma gam e. TheMEA is able to improve upon the outcome of the prisoner’s dilemma, butwhen there are many agen ts, the MEA migh t not be able to achieve fullcooperation. In addition, the MEA is able to sustain (in a sense made precisebelow ) a smaller amount of cooperation in exactly the situation wher e thepotential b enefits of cooperation are greater.The MEA leads to som e impro vement (relative to the pr isoner ’s dilemm a)because it provid es a vehicle for coun tries to m ake commitm ents. In themodel described here, the success of the MEA is limited (relative to fullcooperation) because the MEA does not completely solve the commitm entproblem.We begin with a two-person prisoner’s dilemma .IX\Y abate polluteabate 1,1 -1,2pollute 2,-1 0,0Table 1: The 2 person prisoner’s dilemmaEach of t wo agents (think of these as countries) has a choice between abatingor polluting. Table 1 shows the pay offs in a game between t wo agen ts, Xand Y. Eac h agent has a c hoice between polluting and abating. X’s actionsare in the row s and Y’s in the colum n s. X’s pa yoff is the first entry and M r.1Y’s the second entry. Thus, if X chooses to abate and Y chooses to pollute,X’s pay off is -1 and Y’s payoff is 2.In this game, eac h player’s dominant strategy (definedasanactionthatisoptim al regardless of what the other player does) is to pollute, so the uniqueNash equilibrium is for both pla yers to pollute. The ir collective w elfarew ould be higher if eac h pla yer abated. Here, individual rationalit y does notlead to a good collectiv e outcom e.Now we will consider a particular "participation game" that uses thepriso ne r’s dilemm a game as a building block . Since we are still in a two -agen t setting, this model does not provide a good description of m ultilateralME A s, but it is useful for explaining the in tu ition . Here is the three-stageparticipation game. In the first stage, agen ts decide w hether to join a ME A .In this setting the n u mber of MEA signatories can be 0, 1 or 2. In thesecond stage, the agent(s) in the MEA reach a collective agreement, onethat maxim izes the gr oup welfare of MEA members.Inthethirdstage,non-m embers act to maxim ize their individual self-interest.Dyn am ic problems like this one must be solved "ba ckw ar ds" , i.e. startingfrom the last stage. Agen ts who can mo ve first need to under stand the co nse-quence of their action s; we can determine these consequences by "backwa rdsinduction".. In this particular game, where there is a dom inant strategy,non-m embers alwa ys decide to pollute. Therefore, no matter what the num-ber of agents in the MEA , non-mem bers alw ays pollute. The solution to thethird stage of the problem is therefore simple.Now mo ve back to the second stage. We need to figureouthowtheMEAwill behav e, as a function of the n u mber of agen ts who signed the MEA . If0 agents signed the ME A, there is nothing to decide. If one agent signedthe MEA, the group w elfare of MEA mem bers is the sam e as the individualwelfare of the single member. Therefore, an MEA that consists of a sing leagent alwa ys decides to pollute. An MEA that consists of two agen ts decidesthat both agents must abate.No w consider the first stage of the game, when agents decide whetherto join the MEA. To find the N ash equilibriu m , we need to find the bestresponse, for each agent, to the action of the other agen ts. Table 2 sho w sthe actions and payoffs. The action "join ME A " is a (w e akly ) domina ntaction, meaning that the payoff under that action is at least as high as thepa y off under the other action no ma tter what the other agent does.2x\yjoinMEAdon’tjoinjoin MEA 1 ,1 0,0don’t join 0,0 0,0Table 2: T he MEA gameIn this case, the unique equilibrium is for both agents to sign the agree-ment. The MEA solves the prisoner’s dilemma, because it enables agents toconditio n their abate/pollute decision on actions that other agents take.No w I w ant to explain why, when there are man y agen ts, an MEA (of thet ype considered here) ma y not be able to sustain full cooperation. Supposethat there are N countries. Eac h country decides whether to abate or topollute. The cost of abatement for eac h country is c; every country obtainsb for each county that abates. If k other coun tries hav e decided to abate,then if I decide to abate also, there will be k +1 abaters, and m y pa yoff is(k +1)b−c. If I decide not to abate, m y pay off is kb. The parameter c is theprivate cost of abatement, and the param eter b determ ines the magnitude ofthe externality. E ach additional abater increases aggregate benefits b y Nb.We assume that b<c. This inequalit y means that "pollute" is a domi-nant strategy in the third stage of the gam e (where the non-m ember chooseswhether to pollute or to abate). To confirm this assertion, note the differ-ence between the payoff of an agen t who pollutes, and an agent who abatesis kb − [(k +1)b − c]=c − b>0.Thedifference in the pa yoffs depend son param eter values, not on the nu mber of agents who pollute. The bestresponse for an y agent, taking as giv en the pollute/abate decisions of otheragents,istopollute. Thisiswhatitmeanstosaythat"pollute"isadomi-nant strategy. Suppose also that global w elfare is higher if ev e ryone abates;this condition requires N>cb.For example, suppose that N =5, b =2and c =3.Graphthepayoffto an agen t who pollutes, ΠP(k) as a function of the number of agents whoabate (k)andthepayoff to an agent who abates,
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