Georges Zaccour Chair in Game Theory and Management, GERAD, HEC Montréal, Canada 1Georges Zaccour Universidad de Valladolid

 Some generalities on IEAs  Game theory 101  IEA as a non-cooperative game  IEA as a cooperative game Georges Zaccour Universidad de Valladolid2

 n countries (transboundary context)  Interdependent payoffs  Examples: tropical forest, biodiversity, fisheries, emissions reduction, etc.  Asymmetry  Benefits  Costs  Views on means to be deployed  Long-term problem (inertia in technology and behavior) Georges Zaccour Universidad de Valladolid3

Some treaties:  Climate change (Kyoto Protocol, COP 15)COP 15  Ozone layer depletion (Montreal Protocol)Montreal Protocol  Acid rain (Sulphur Emissions Reduction Protocol)Sulphur Emissions Reduction Protocol  Biodiversity loss (Biodiversity Convention)Biodiversity Convention 4Georges Zaccour Universidad de Valladolid

Typical features of many environmental problems: Public good, Externalities, Free riding ExcludableNon-excludable Rivalrous Pure private goodOpen-access resource (common good) Ocean fishery Non-rivalrous Club good Wilderness Area Public good Air, Pollution abatement 5Georges Zaccour Universidad de Valladolid

 Externalities: one agent’s decision has an impact on utility of other agents in an unintended way and when no compensation/payment is made by the generator.  Free riding  Provision of a public good usually leads to Market Failure  No international institution to correct this; voluntary international cooperation efforts to provide the public good. 6Georges Zaccour Universidad de Valladolid

 Branch of mathematics  Applications in many areas: Economics, politics, engineering, biology, ecology, computer science, etc.  Strategic Interactions between players (firms, countries, automata, etc.)  Payoff of one depends on what the others do  Optimization problem vs. game problem Georges Zaccour Universidad de Valladolid7

 Cooperative vs. non-cooperative games  Description of a game  Normal or strategic form  Extensive form  Characteristic function form Georges Zaccour Universidad de Valladolid8

Game in strategic form:  Set of players  Strategic players, dummy players (e.g., nature)  Set of strategies of each player  Payoffs  Function of selected strategies by all players Georges Zaccour Universidad de Valladolid9

Further assumptions:  Each player is rational  Common knowledge that each player is rational  Information: Perfect / imperfect; Complete / incomplete 10Georges Zaccour Universidad de Valladolid

 Non-cooperative game: Nash equilibrium  No player has an interest in deviating unilaterally  Best response (BR) to other players’ strategies  Existence: Strategy set is compact and convex; payoff is continuous and quasi-concave in own strategy; proof relies on a fixed-point argument of BR  Uniqueness: BR is a contraction Georges Zaccour Universidad de Valladolid11

 Non-cooperative approach  Voluntary participation  Club idea  Mechanisms to increase participation  Cooperative approach  Collective optimum  Sharing of benefits (and costs) Georges Zaccour Universidad de Valladolid12

Prisoners’ Dilemma -1, -1 -9, 0 0, -9 -6, -6 Prisoner 2 Prisoner 1 Not Confess Confess Not Confess Confess Normal form representation: agents choose their strategy simultaneously 13Georges Zaccour Universidad de Valladolid Prisoners’ Dilemma

Pollution’s Dilemma -1, -1 -9, 0 0, -9 -6, -6 Prisoner 2 Prisoner 1 AbatePollute Abate Pollute Pollute is the dominant strategy for each player 14Georges Zaccour Universidad de Valladolid Prisoners

 Two drivers drive towards each other on a collision course: one must swerve, or both may die in the crash, but if one driver swerves and the other does not, the one who swerved will be called a "chicken," meaning a coward;  Hawk-Dove refers to a situation in which there is a competition for a shared resource and the contestants can choose either conciliation or conflict. Georges Zaccour Universidad de Valladolid15

Georges Zaccour Universidad de Valladolid16 0, 0-100, , , Swerve Do not swerve Swerve Do not swerve

Georges Zaccour Universidad de Valladolid17 0, 0-100, , , Abate Pollute Abate Pollute

Country 1 Country 2 pollute abate pollute abate pollute (-4, -4) (5, -2) (-2, 5) (3, 3) Which equilibrium will be played? Extensive form game: sequential choice leads to a unique Nash Equilibrium Backward induction „First-Mover advantage“ 18Georges Zaccour Universidad de Valladolid

„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 haven: Yale University Press, pp: ] 19Georges Zaccour Universidad de Valladolid

0, 0 0, -8 -8, 0 4, 4 Country 2 Country 1 Do not contribute Contribute Do not contribute Contribute Cost of contribution Benefit of contribution (only if both countries contribute) Two Nash equilibria Cooperative solution is stable 20Georges Zaccour Universidad de Valladolid

 Cartel (club) problem  Entry test  Exit test  Self enforcing: no participant has an incentive to deviate and no non-participant has an incentive to accede to the agreement  Size of the agreement: how many countries will join? 21Georges Zaccour Universidad de Valladolid

 Different payoff structures lead to different equilibria.  Signatories and non-signatories would both do better if all cooperate (prisoners’ dilemma)  Non signatories do better than the signatories, because they free-ride (chicken game)  Full cooperation is not usually stable (it is not self enforcing) 22Georges Zaccour Universidad de Valladolid

 How can international treaties be structured, such that the mutually preferred outcome is an equilibrium?  Repeated games: cooperative equilibria become reachable  Fraction of members decreases when there are many countries affected  Breadth versus depths of an agreements  Modest target? 23Georges Zaccour Universidad de Valladolid

 Literature: 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  How can the incentive structure be manipulated? 24Georges Zaccour Universidad de Valladolid

 Existence of an external institution which coordinates the process  Leadership role by one important nation  Define minimum participation threshold (e.g., Kyoto) 25Georges Zaccour Universidad de Valladolid

 Side payments to induce cooperation of the non contributors  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. 26Georges Zaccour Universidad de Valladolid

 Starting point: No obstacles to cooperation (economic, sociological, psychological, political, etc.)  Two-step algorithm 1. Det ermine the best collective outcome 2. Share this outcome Georges Zaccour Universidad de Valladolid27

 Characteristic function  measure of strategic force of coalitions  Set of Imputations  individual and collective rationality  Solutions  Value-type solutions (unique imputation)  Set of imputations Georges Zaccour Universidad de Valladolid28

 Core: stable allocation (but core can be empty)  Shapley Value (linearity, Pareto-optimality, fairness)  Each player gets a weighted average of her marginal contributions Georges Zaccour Universidad de Valladolid29

 Horizontal equity: One man, one vote  Vertical equity: Altruism  Market justice: Efficient allocation of resources  Sovereignty: No invasion of a player’s right  Consensus : Diplomacy  Compensation : Extension of Pareto...  Principle of Rawls : Horizontal + vertical  Shapley value: Symmetry, strategic force Georges Zaccour Universidad de Valladolid30

 Dynamic problem: long-term agreement  How to guarantee sustainability?  Binding agreement  Time-consistent agreement  Cooperative equilibrium  Mechanisms: Side payments, punishment, threat, etc. Georges Zaccour Universidad de Valladolid31

 Incentive Strategies  I behave as a gentleman if you do the same (tooth for tooth, eye for eye)  Incentive equilibrium  Credibility  Two-player context Georges Zaccour Universidad de Valladolid32

 Agreement to punish a deviator  Based on past behavior  Random events  Discontinuities Georges Zaccour Universidad de Valladolid33

 Design an agreement  cooperative payoff-to-go dominates non- cooperative payoff-to-go  Not an equilibrium: a minimal requirement Georges Zaccour Universidad de Valladolid34

 Shed a light on a series of questions:  Will countries behave selfishly and continue to pollute?  Does mutually beneficial cooperation take place between independent states?  What can be done to increase the chances of cooperative behavior? Georges Zaccour Universidad de Valladolid35

 Modeling payoff functions  Measure of damages  Techno-economic models and large-scale optimization models  Learning  Non linearities (almost in everything!)  Correlations between pollutants Georges Zaccour Universidad de Valladolid36

 Jorgensen, Martín-Herrán, Zaccour (2010)  Zaccour (2008)  Breton, Sbragia, Zaccour (2010)  Other papers in forest mangement, climate- change negotiation, etc. Georges Zaccour Universidad de Valladolid37