Game Theory and International Environmental Agreements IEA christine.heumesserboku.ac.at

1. Game Theory and International Environmental Agreements (IEA) christine.heumesser@boku.ac.at

2. Outline of lecture Introduce 3 games which reflect challenges an IEA is facing. Outline methods of operation of Game Theory (equilibrium concepts, simultaneous and sequential moves, mixed strategies, repeated games and games with many players) Show how Game Theory can serve as tool/framework to approach international environmental problems

3. Game theory and International Environmental Agreements International environmental problems and their treaties: i.e.: Climate change (Kyoto Protocol) Ozone layer depletion (Montreal Protocol) Acid rain (Sulphur Emissions Reduction Protocol) Biodiversity loss (Convention on Biological Diversity)

4. Game theory and International Environmental Agreements Typical features of many environmental problems (Public good, Externalities, Free riding) can be handled by means of game- theoretic models and framework.

5. Game theory and International Environmental Agreements Externalities: occur when the production or consumption decision of one agent has an impact on the utility or profit of another agents in an unintended way and when no compensation/payment is made by the generator. Provision of a public good usually leads to Market Failure no international institution to correct this; instead voluntary international cooperation efforts to provide the public good.

6. Game theory and International Environmental Agreements Following Questions arise:

7. Game Theory? Sub discipline of Mathematics Focuses on games where There are 2 or more players Some choice of action where strategy matters Outcome for each player depends on the strategy chosen by all other players offers an approach to model the strategic interactions among economic agents attempts to capture behavior in strategic situations, in which an individual's success depends on the choices of others

8. Game Theory? Many economic issues involve strategic interaction. � Behavior in imperfectly competitive markets, e.g. Coca-Cola versus Pepsi. � Behavior in auctions, e.g. Investment banks bidding � Behavior in environmental/economic negotiations Got popular in 1944 after the publication of �Games and Economic Behaviour� by John von Neumann and Oskar Morgenstern Several game theorists won the Nobel Prize, u.o.: Robert Aumann, Thomas Shelling, John Harsanyi, John F. Nash Jr. (�A beautiful mind� by Silvia Nasar), Reinhard Selten

9. Game Theory? Three Elements of a Game: 1) The players: � how many players are there? � does nature/chance play a role? 2) A complete description of the strategies of each player 3) A description of the consequences (payoffs) for each player for every possible profile of strategy choices of all players.

10. Game Theory? Further assumptions for following games: (4.) Assumption that each player is rational (5.) Common knowledge that each player is rational (6.) Perfect information: the payoff functions are common knowledge. In an EQUILIBRIUM, each player of the game has adopted a strategy that they are unlikely to change

11. Games which depict an IEA Prisoners� Dilemma

12. Games which depict an IEA

13. Equilibrium Concepts Strictly dominated strategies are not always given:

14. Equilibrium Concepts Nash Equilibrium: In the n-player normal-form game a strategy is a Nash Equilibrium if it is for each player the best response to the strategies specified for the other players. In the previous games the non-cooperative solutions (pollute, pollute) and (confess, confess) are Nash equilibria. Each normal form game has at least one Nash equilibrium. What happens if there are several Nash equilibria?

15. Games which depict an IEA Pollution Game 2 (analogue to Chicken Game):

16. Games which depict an IEA Pollution Game 2 (analogue to Chicken Game):

17. Games which depict an IEA First-mover advantage: �The lady who pushes her child�s stroller across the intersection in front of a car that has already come to a dead stop is in no particular danger as long as she sees the driver watching her: even if the driver prefers not to give her the right of way she has the winning tactic� [Schelling (1966). Arms and Influence. New have: Yale University Press, pp: 117-118]

18. Games which depict an IEA Pollution Game 2 (analogue to Chicken Game): How to figure out which strategy will be played when the game is played simultaneously? Assume a probability distribution over each strategy.

19. Games which depict an IEA Pollution Game 3 (analogue to the Assurance Game):

20. different payoff structures lead to different equilibria. How can international treaties be structured, such that the mutually preferred outcome is an equilibrium?

21. Repeated games Until now we only looked at one-shot games, what happens when games are played repeatedly? Players have to take into account the future actions of other players Players act differently; also cooperative solutions are possible. Outcome depends on the future valuation of the players (discount rate) Infinitely repeated games Finitely repeated games

22. Repeated games (Infinitely repeated games) There are two possible actions: �good� and �bad� Examples of strategies: Stable (always plays bad) Pendulum (alternately good and bad, irrespective of opponent) Trigger (starts of nice and plays good as long as opponent plays good; if disappointed plays bad forever after) Imitate (starts off with good and then observes opponent and imitates his action of previous period) These are strategies where cooperation can be sustained.

23. Repeated games (Infinitely repeated games) Examples: Stable vs. Trigger:

24. Multiple players Prisoners� Dilemma with multiple players, N= 10 Pollution abatement costs 7 and confers a benefit of 5 to countries

25. Multiple players Prisoners� Dilemma with multiple players, N= 10 Another payoff structure (a=12, b= 3, c = -7, d= 7)

26. Multiple players and partial agreements If multiple players are involved: also partial cooperation is possible. In this case, an agreement must be self-enforcing Self enforcing: no participant has an incentive to deviate and no non-participant has an incentive to accede to the agreement.

27. Which conclusions can be drawn from Game Theory for the functioning of IEAs? Signatories and non-signatories would both do better if all cooperate (like in the prisoners� dilemma) Non signatories do better than the signatories, because they free-ride (similar to the chicken game) Full cooperation is not usually stable (it is not self enforcing) Fraction of members decreases when there are many countries affected. Breadth versus depths of an agreements

28. Which conclusions can be drawn from Game Theory for the functioning of IEAs? Predictions for self-enforcing agreements are rather pessimistic. Since treaties must be self-enforcing, they must do more than simply telling countries what to do. Treaties must manipulate the incentive structure of countries (Barrett, 2003: 18) How can the incentive structure be manipulated?

29. Which conclusions can be drawn from Game Theory for the functioning of IEAs? Existence of an external institution which coordinates the process. Leadership role by one important nation. Define minimum participation threshold. side payments to induce cooperation of the non contributors (Montreal protocol) Establish more agreements than only one. For instance for each group of countries which has particular characteristics; Kyoto protocol and developing countries Linkage of negotiations and linked benefits.

30. Literature suggestions Introduction to Game theory: Gibbons, Robert (1992). A Primer in Game Theory. Harvester: Wheatsheaf Binmore, Ken (1991). Fun and Games. A text on game Theory. D.C. Heath Game Theoretic Literature on IEAs: Barrett, Scott (1994a). �Self-Enforcing International Environmental Agreements.� Oxford Economic Papers, 46, 878-894. Barrett, Scott (1998b). �Political Economy of the Kyoto Protocol.� Oxford Review of Economic Policy, 14, 20-39 Barrett, Scott (2003): Environment & Statecraft. The strategy of environmental treaty making. Oxford University Press Cesar, H. and de Zeeuw, A. (1996). Issue linkage in global environmental problems. In Xepapadeas, A., ed.: Economic Policy for the Environment and Natural Ressources. E. Elgar, Cheltenham. Carraro, Carlo and Dominico Siniscalco (1993). �Strategies for the International Protection of the Environment.� Journal of Public Economics, 52, 309-328. Carraro, Carlo (ed., 2003): Governing the Global Environment. E. Elgar, Cheltenham, Finus, M. (2003). Stability and design of international environmental agreements: The case of transboundary pollution. In Folmer, H. and Tietenberg, T.; ed.: International Yearbook of Environmental and Resource Economics, 2003/4, E. Elgar, Cheltenham www.feem.it Fondazione Eni Enrico Mattei has many working papers on this topic.

31. Literature suggestions Experimental Game Theory: Axelrod, Robert (1986). The evolution of cooperation. New York: Basic Books Benz, Matthias and Meier, Stephan (2008). Do People Behave in Experiments as in the Field? Evidence from Donations. Experimental Economics. Volume 11, Number 3 Camerer, Colin�(2003):�Behavioral game theory��:�experiments in strategic interaction. �New York, NY��:�Russell Sage Foundation Diekmann (1993) .Cooperation in an Asymmetric Volunteer�s Dilemma Game: Theory and Experimental Evidence. International Journal of Game Theory. Volume 22, Number 1 Fischbacher, Urs; G�chter, Simon; Fehr, Ernst (2001). Are people conditionally cooperative? Evidence from a public goods experiment. pp 397-404 Fischbacher, Urs and G�chter, Simon (2005). Heterogeneous social preferences and the dynamics of free riding in public goods. IEW Working Paper, iewwp 261, Institute for Empirical Research in Economics- IEW Fehr, Ernst and Fischbacher, Urs (2004). Social norms and human cooperation. Trends in Cognitive Science, Volume 8, Issue 4, pp. 185-190 Schelling, Thomas (1997). �The strategy of conflict:�Cambridge, Mass. :�Harvard Univ. Press� Sigmund, Karl and Nowak, Martin (1999). Evolutionary Game Theory. Current Biology, Volume 9, Issue 14, p. 503-505