REM 621 TOPIC 17: TRANSBOUNDARY POLLUTION PROBLEMS

1. REM 621TOPIC 17: TRANSBOUNDARY POLLUTION PROBLEMS

2. Introducing ‘Game theory’ • Defn. Game theory – “the study of multi-agent decision problems" • Players simultaneously choose an action but in doing so they take into account the possible actions of others • Must specify: • the players • the strategies available to each player • the payoffs for each player for each combination of strategies that can be selected

3. Game Theory: Basic Concepts Some concepts: • static games vs. dynamic games (e.g. repeated games) • cooperative games vs. non-cooperative games • perfect vs. imperfect information • complete vs. incomplete information Sample games: • Prisoners’ Dilemma • Chicken Game • Assurance Game

4. A. Strict Domination: the Pastoralist Tragedy of the Commons as a Static Prisoners’ Dilemma Game Source: adapted from Bojo et al.

5. B. Iterated Elimination of Strictly Dominated Strategies Source: Gibbons 1992, Fig. 1.1.1.

6. Iterated Elimination of Strictly Dominated Strategies (continued) Source: Gibbons 1992, Fig. 1.1.2.

7. Iterated Elimination of Strictly Dominated Strategies (continued) Source: Gibbons 1992, Fig. 1.1.3.

8. Can you find Strictly Dominated Strategies here? Source: Gibbons 1992, Fig. 1.1.4.

9. There are no Strictly Dominated Strategies to eliminate Source: Gibbons 1992, Fig. 1.1.4. Now what? We call on a weaker solution concept … Defn. Nash Equilibrium - each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his or her own strategy unilaterally.

10. C. Finding the Nash Equilibrium

11. Nash Equilibrium - Class Exercise Source: Gibbons 1992, p. 7-8.

12. Class Exercise - Solution Source: Gibbons 1992, p. 7-8.

13. Nash Equilibrium Concept Fig 7.8, Hanley et al. 2001

14. Ordinal Form of Prisoners’ Dilemma B’s strategy A’s strategy Note: 4 > 3 > 2 > 1

15. D. Classic Chicken game – ordinal payoffs B’s strategy A’s strategy Note: 4 > 3 > 2 > 1

16. Classic Chicken game – Solution B’s strategy A’s strategy Note: 4 > 3 > 2 > 1

17. Pollution Case (Public Good) B’s strategy A’s strategy Assumptions: benefits are additive and shared (public good aspect) at 6 ea; cost of contribution is 8 ea; free riding can occur Source: Sandler 1997, p. 38.

18. D. Assurance Game B’s strategy A’s strategy Assumptions: benefits are additive and shared (public good aspect) but no benefit unless both contribute; cost of contribution is 8 ea; no free riding; worst case with no contributions is 0 vs. -5 Source: Sandler 1997, p. 34.

19. Assurance Game - Solution B’s strategy A’s strategy Source: Sandler 1997, p. 34.

20. Prisoners’ Dilemma as a Repeated Assurance Game Source: adapted from Bojo et al.

21. Prisoners’ Dilemma as a Repeated Assurance Game Source: adapted from Bojo et al.

22. E. Full Cooperative Solution B’s strategy A’s strategy Source: Sandler 1997, p.45.

23. Full Cooperative - Solution B’s strategy A’s strategy Source: Sandler 1997, p.45.

24. An Example: “The Acid Rain Game”

25. Lessons for Climate Change • true public good (vs. acid rain deposition) • benefits uncertain (?) and distant but prevention/mitigation costs now • few local benefits • significant opportunities to free ride • lead player (USA) has little selective incentive (negative net benefits)