Stephan Dohrn, CAPRi

1. The Experimental GameBasic Game Theory for Natural Resource Management Stephan Dohrn, CAPRi

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

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

4. Terminology, cont’d • 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 • Common Pool Resources:– partial excludability, rivalry • Social Optimum/Joint maximization

5. Classification of Goods Rivalry High Low Excludability Common Pool Resources Public Goods No Club Goods Private Goods Yes

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

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

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

9. Recap: A Game is described by • 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 utility function u = {u1, ..un} • In case of cooperative game theory also the (implicit) rules.

10. 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 and NC, nc – C, nc > 0 NC, c – C, c > 0 and NC, nc – C, nc < 0 NC, c – C, c < 0 and NC, nc – C, nc < 0 and C, c > NC, nc NC, c – C, c > 0 and NC, nc – C, nc > 0 and C, c < NC, nc

11. 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 • Technology Adoption: Must consider management of natural resources and impact on adoption. Could explain a lot!

12. Things We Haven’t Discussed • 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. • 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.

13. 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. • 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.