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# EC4004 Lecture 6 Risk and Game Theory

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### EC4004 Lecture 6 Risk and Game Theory

1. 1. EC4004 Lecture 6 Probability and Game Theory Dr Stephen Kinsella
2. 2. A Panda is for life. Not Just for The Debs.
3. 3. Today
4. 4. 1. Risk
5. 5. 2. Insurance
6. 6. 3. Game Theory
7. 7. Yesterday
8. 8. 1. Risk
9. 9. 4 Ideas:
10. 10. 1. Probability: Average Frequency of events
11. 11. 2. Expected value of game with a number of uncertain outcomes: size of prize player will win on average.
12. 12. 3. Fair games are games that cost precisely their expected value.
13. 13. 4. Risk aversion is tendency for people to refuse to accept fair games.
14. 14. Combine 4 ideas with Diminishing Marginal Utility to get:
15. 15. Utility U 0 20 30 33 35 40 50 Income (thousands of euros)
16. 16. Utility U 0 20 30 33 35 40 50 Income (thousands of euros) Here’s a person a person with three options. Contender may: 1. retain current income level (€35,000) without taking any risk; 2. take a fair bet with a 50-50 chance of winning or losing €5,000; 3. take a fair bet with a a 50-50 chance of winning or losing €15,000.
17. 17. 2. Insurance
18. 18. Utility U U1 Income 0 20 25 35 (thousands of euros)
19. 19. Utility U U1 Income 0 20 25 35 (thousands of euros) Assume that during next year a person with €10,000 current income faces a 50 percent chance of incurring €4,000 in unexpected medical bills. Without insurance, the person’s utility would be U1, - i.e. the utility of the average of €6000 and €10,000.
20. 20. 3. Game Theory
21. 21. Study of Strategic Interaction
22. 22. Study of Strategic Interaction
23. 23. 3 Components to Any Game
24. 24. 1. Players
25. 25. 2. Payoffs
26. 26. 3. Strategies
27. 27. Equilibrium
28. 28. A Nash equilibrium is a set of strategies, one for each player, that are each best responses against one another.
29. 29. In a two-player games, a Nash equilibrium is a pair of strategies (a*,b*) such that a* is an optimal strategy for A against b* and b* is an optimal strategy for B against A*.
30. 30. A Beautiful Mind
31. 31. Next Time: More Game Theory Iterated Prisoners Dilemma Try 6.1, 6.3, 6.5
32. 32. EC4004 Lecture 6 Probability and Game Theory Dr Stephen Kinsella