Time-Consistency and Environmental Efficiency of Closed International Agreements (IEA)

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 • 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). Structure of Coalition Formation in Membership Models* (Chandler,Tulkens) *free-riders – those who deviate from participation (other option – deviate from commitment) at the moment, plan to be contribute

3. Problem • characterize initial (t=0) abatement commitments ej and propose optimal abatement scheme in dynamics ej([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. Model 2-level multistage coalitional game with perfect information (players are familiar with type of others, 2-level model means 1st level (leader) – coalition, 2nd level (follower) –free-riders where t=1,…m, N – heterogeneous players (nations), K groups, - players’ abatement targets, j=1,…,N, and E= Σ ej, - net benefit. Key concepts3,12 Self-enforcing coalition 1. internal stability 2. external stability • Time-consistency of self-enforcing coalition • internal time-consistency • external time-consistency

4. Results • Analytical solution of abatement commitments (a,b,ci,n,N) • - positive and finite (as Stackelberg equilibrium); • Optimal abatement scheme (Stackelberg solution coincides wish Nash equilibrium) • for t=0,…,m-1 • Specification of time-consistency conditions of coalition and abatement solution for the multistage model; • A threshold level of size n' of coalition S to be environmental efficient*; • Time-consistency of a closed coalition**, • if coalition size > n'; • Time-consistency of abatement scheme (Stackelberg solution). * 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

5. Further Plans • 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). *life-circle means length of period [0,m]

6. Reference • A. Kryazhimskii, A. Nentjes, S. Shibayev, A. Tarasyev (1998) Searching Market Equilibria under Uncertain Utilities, INTERIM REPORT IR-98-007 / February • 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 • L. Petrosjan (1977) Stability of solutions in n-person differential games, Bull. Leningrad University, vol. 19. pp. 46 – 52. (Russian) • V. Zakharov,M. Dementieva (2004) Multistage cooperative games and problem of time consistency. Int. Game Theory Rev. 6, no. 1,pp. 157-170. • C. Carraro, D. Siniscalco (1993) Strategies for the international protection of the environment, Journal of Public Economics vol. 52, pp. 309-328 • S. Barrett (1994) Self-Enforcing International Environmental Agreements, Oxf. Econ. Papers. 46. pp. 878 – 894. • 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. • S. Rubio, A. Ulph (2003) An Infinite-Horizon Model of Dynamic Membership of International Environmental Agreements, Nota di lavoro 57.2003 • P. Chandler, H. Tulkens (2006) Cooperation, Stability and Self-Enforcement in International Environmental Agreements: A Conceptual Discussion, CORE Discussion Paper 2006/03 • 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. • 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. • C. D’Aspremont, A. Jacquemin, J. A. Weymark (1983) On the Stability of Collusive Price Leadership, Can. J. Econ., Vol. 16. pp. 17 – 25. • 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.