Stephan Dohrn, CAPRi The Experimental Game Basic Game Theory for Natural Resource Management

Outline Terminology Terminology Game Structures Game Structures Empirical Examples, and Game-Theoretic Results Empirical Examples, and Game-Theoretic Results A Few Games in Detail A Few Games in Detail Conclude with things we haven’t touched on, but may be relevant Conclude with things we haven’t touched on, but may be relevant

Terminology Externalities Externalities Non-Cooperative Game Theory vs. Cooperative Game Theory Non-Cooperative Game Theory vs. Cooperative Game Theory Strategy Set & Actions Strategy Set & Actions Equilibria (F&T) Equilibria (F&T)

Terminology, cont’d Public Goods: Goods or services whose benefits are non-excludable and non-rival (C&S). Public Goods: Goods or services whose benefits are non-excludable and non-rival (C&S). “Impure” Public Goods: Goods or services whose benefits are partially excludable and/or rival “Impure” Public Goods: Goods or services whose benefits are partially excludable and/or rival Common Pool Resources:– partial excludability, rivalry Common Pool Resources:– partial excludability, rivalry Social Optimum/Joint maximization Social Optimum/Joint maximization

Classification of Goods Public Goods Private Goods Club Goods Common Pool Resources ExcludabilityExcludability Rivalry Yes No Low High

What is Game Theory Formalized language to analyze decision-making situations. Formalized language to analyze decision-making situations. Results depend on decisions AND estimated probabilities of the players Results depend on decisions AND estimated probabilities of the players Players are conscious about the interdependency. Players are conscious about the interdependency. Every player takes into account above conditions. Every player takes into account above conditions. Game theory in NRM? Game theory in NRM?

Incentives and Interdependency Cooperate Not Cooperate R=3 T=4 S=0 T=4 P=1 Cooperate Not Cooperate T=Temptation; R=Reward; P=Penalty; S=Sucker

Incentives and Interdependency Cooperate R R T S S T P P Not Cooperate T=Temptation; R=Reward; P=Penalty; S=Sucker NC, c – C, c > 0 Incentives to Cheat: Incentives not to be Suckered: NC, nc – C, nc > 0 Not Cooperate

Recap: A Game is described by The set of players N = {1,...n}; The set of players N = {1,...n}; The strategy Space S, defined as the set of all possible combinations of strategies s = {s1,..sn} of the single players The strategy Space S, defined as the set of all possible combinations of strategies s = {s1,..sn} of the single players The utility function u = {u1,..un} The utility function u = {u1,..un} In case of cooperative game theory also the (implicit) rules. In case of cooperative game theory also the (implicit) rules.

A Few Game Structures A Few Game Structures Prisoner’s Dilemma: Assurance Game: Chicken Game: Fully Privileged (or Un-Privileged): NC, c – C, c > 0 and NC, nc – C, nc > 0 NC, c – C, c 0 NC, c – C, c > 0 and NC, nc – C, nc < 0 NC, c – C, c NC, nc NC, c – C, c > 0 and NC, nc – C, nc > 0 and C, c < NC, nc

Wait, what’s the point again? Evaluate: Is group optimally managing the natural resource base? If not, is it because of individual incentives? If so, organizational structure and institutional design need to be tailored to incentive structure Evaluate: Is group optimally managing the natural resource base? If not, is it because of individual incentives? If so, organizational structure and institutional design need to be tailored to incentive structure Technology Adoption: Must consider management of natural resources and impact on adoption. Could explain a lot! Technology Adoption: Must consider management of natural resources and impact on adoption. Could explain a lot!

Things We Haven’t Discussed Asymmetric Externalities (upstream/ downstream users of river; beekeeper/orchard grower; crops/livestock) Asymmetric Externalities (upstream/ downstream users of river; beekeeper/orchard grower; crops/livestock) Repeated & Dynamic Games – Prisoner’s Dilemma “is transformed” into an Assurance Game, for instance. Dynamic externalities likely to be important for soil erosion control, reforestation, etc. Repeated & Dynamic Games – Prisoner’s Dilemma “is transformed” into an Assurance Game, for instance. Dynamic externalities likely to be important for soil erosion control, reforestation, etc. Uncertainty: Can ‘o Worms. Undertaking any activities to improve returns in highly variable environments will be lower than in more stable environments; but exploitation rates will be lower, too. Uncertainty: Can ‘o Worms. Undertaking any activities to improve returns in highly variable environments will be lower than in more stable environments; but exploitation rates will be lower, too.

Things We Haven’t Discussed Discrete Games: Basically, these are pretty easy, and much more in extant literature. Lump-sum investments likely to have Assurance Game incentive structure, but you can get nearly anything. Discrete Games: Basically, these are pretty easy, and much more in extant literature. Lump-sum investments likely to have Assurance Game incentive structure, but you can get nearly anything. Different Game Forms: Weakest Link, Strongest Link (these likely to result from Discrete Games, though) Different Game Forms: Weakest Link, Strongest Link (these likely to result from Discrete Games, though) More Than One Strategic Choice Variable: Examples include animal health and stock densities; reforestation and soil erosion control; road maintenance on fishing effort, etc. More Than One Strategic Choice Variable: Examples include animal health and stock densities; reforestation and soil erosion control; road maintenance on fishing effort, etc.