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

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

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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

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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

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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

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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

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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

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

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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

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

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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

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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

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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

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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

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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

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

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

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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

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„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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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

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

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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

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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

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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

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