1. Time-Consistency and Environmental Efficiency of Closed International Agreements (IEA) Yulia Pavlova jupavlov@cc.jyu.fi Researcher, MSc, Dept. of Mathematical Information Technology, University of Jyväskylä, Finland Supervisors:PhD Maria Dementieva (University of Jyväskylä) Prof. Victor Zakharov (St.Petersburg State University) Prof. Pekka Neittaanmäki (University of Jyväskylä)

2. Research Background Structure of Coalition Formation in Membership Models* (Chandler,Tulkens) 1 st Stage: participation SequenceSimultaneous (Yi ) (no revision of members) Sequential (Carraro ) (revision of members) AgreementsSingle (Carraro, Barrett, Yi) Multiple (Finus, Yi.) MembershipOpen (Carraro, Barrett, Yi ) exclusive (majority, unanimity) (Yi ) 2 nd Stage: abatement and transfers Sequence simultaneous (Cournot,Nash) (Yi ) sequential (Stackelberg) Abatementsjoint welfare maximization (efficient) (Carraro, Barrett, etc.) bargaining (majority, unanimity) (Tarasyev) Transfersnoyes (Tarasyev) Payoffssocial planner/ material/ certain ( Yi, Barrett, Pavlova, etc.) political/ non-material/ uncertain ( Tarasyev ) *free-riders – those who deviate from participation (other option – deviate from commitment) at the moment, plan to be contribute Agreement modeling as a coalition of players:  non-cooperative (Carraro, Barrett) or cooperative (Petrosjan, Zakharov),  static (Carraro, Barrett, Tarasyev) or dynamic (Zaccour, Kaitala, Zakharov, Ulph).

3. Model 2-level multistage coalitional game with perfect information (players are familiar with type of others, 2-level model means 1 st level (leader) – coalition, 2 nd level (follower) –free-riders where t=1,…m, N – heterogeneous players (nations), K groups, - players’ abatement targets, j=1,…,N, and E= Σ e j, - net benefit. Problem characterize initial (t=0) abatement commitments e j and propose optimal abatement scheme in dynamics e j ([t,m]), t=0,…,m ; specify coalition structure S of IEA at initial moment t=0 ; explore time-consistency of IEA during t=1,…,m. Key concepts 3,12 Self-enforcing coalition 1. internal stability 2. external stability Time-consistency of self-enforcing coalition 1.internal time-consistency 2.external time-consistency

4. Results 1. Analytical solution of abatement commitments (a,b,c i,n,N) - positive and finite (as Stackelberg equilibrium); 2. Optimal abatement scheme (Stackelberg solution coincides wish Nash equilibrium) for t=0,…,m-1 3.Specification of time-consistency conditions of coalition and abatement solution for the multistage model; * If one player leaves a self-enforcing IEA, total abatement can only reduce; **if at t=0 S is self-enforcing coalition, and at t=1,…m no new members are allowed in, old signatories are free-to leave a)A threshold level of size n' of coalition S to be environmental efficient*; b) Time-consistency of a closed coalition**, if coalition size > n' ; c) Time-consistency of abatement scheme (Stackelberg solution).

5. To continue game-theoretic analysis of existing and being under discussion agreements, it is necessary to address issue of time-consistency of an IEA during its life-cycle* and design such policy measures as financial transfers and delayed payoffs (to promote endogenous cooperation within IEA); to assess agreement life-cycle and players discounted payoffs; to explore time-inconsistent IEA evolution; to introduce uncertainty about payoffs (incomplete information). Further Plans *life-circle means length of period [0,m]

6. Reference 1.A. Kryazhimskii, A. Nentjes, S. Shibayev, A. Tarasyev (1998) Searching Market Equilibria under Uncertain Utilities, INTERIM REPORT IR-98-007 / February 2.V. Kaitala, M. Pohjola,O. Tahvonen (1991) Transboundary air pollution between Finland and the USSR - A Dynamic acid rain game, in: R.P. Hämäläinen and H. Ehtamo (eds.), Dynamic Games in Economic Analysis, Lecture Notes in Control and Information Sciences, vol. 152, pp. 183-192 3.L. Petrosjan (1977) Stability of solutions in n-person differential games, Bull. Leningrad University, vol. 19. pp. 46 – 52. (Russian) 4.V. Zakharov, M. Dementieva (2004) Multistage cooperative games and problem of time consistency. Int. Game Theory Rev. 6, no. 1, pp. 157-170. 5.C. Carraro, D. Siniscalco (1993) Strategies for the international protection of the environment, Journal of Public Economics vol. 52, pp. 309-328 6.S. Barrett (1994) Self-Enforcing International Environmental Agreements, Oxf. Econ. Papers. 46. pp. 878 – 894. 7.M. Breton, K. Freidj, G. Zaccour (2006) International Cooperation, Coalitions Stability and Free Riding in a Game of Pollution Control, The Manchester School vol. 74 no. 1, pp. 103–122. 8.S. Rubio, A. Ulph (2003) An Infinite-Horizon Model of Dynamic Membership of International Environmental Agreements, Nota di lavoro 57.2003 9.P. Chandler, H. Tulkens (2006) Cooperation, Stability and Self-Enforcement in International Environmental Agreements: A Conceptual Discussion, CORE Discussion Paper 2006/03 10.S.-S. Yi (2003) The endogenous formation of economic coalitions: The partition function approach, ch.3, pp. 80-127, in Carraro, C. (ed.), Endogenous Formation of Economic Coalitions, Edward Elgar, Cheltenham. 11.M. Finus, B. Rundshagen (2003) Endogenous Coalition Formation in Global Pollution Control: A Partition Function Approach, ch. 6, pp. 199-243, in Carraro, C. (ed.), Endogenous Formation of Economic Coalitions, Edward Elgar, Cheltenham. 12.C. D’Aspremont, A. Jacquemin, J. A. Weymark (1983) On the Stability of Collusive Price Leadership, Can. J. Econ., Vol. 16. pp. 17 – 25. 13.M. Dementieva, Yu. Pavlova, V. Zakharov (2008) Dynamic Regularization of Self-Enforcing International Environmental Agreement in the Game of Heterogeneous Players, in Petrosjan L. and Mazalov V. (ed.), Game Theory and Applications, Vol. 14., Forthcoming.