EC4004 Lecture 6

Probability and Game TheoryDr Stephen Kinsella

A Panda is for life.

Not Just forThe Debs.

Today

1. Risk

2. Insurance

3. Game Theory

Yesterday

1. Risk

4 Ideas:

Probability: Average Frequency of events

1.

Expected value of game with a number of uncertain outcomes: size of prize player will win on average.

2.

Fair games are games that cost precisely their expected value.

3.

Risk aversion is tendency for people to refuse to accept fair games.

4.

Combine 4 ideas with Diminishing Marginal Utility to get:

U

Income(thousandsof euros)

0 35 40 503020

Utility

33

U

Income(thousandsof euros)

0 35 40 503020

Utility

33

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.

2. Insurance

U

U1

Income(thousandsof euros)

0 25 3520

Utility

U

U1

Income(thousandsof euros)

0 25 3520

Utility

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.

3. Game Theory

Study of Strategic Interaction

Study of Strategic Interaction

3 Components to Any Game

1. Players

2. Payoffs

3. Strategies

Equilibrium

A Nash equilibrium is a set of strategies, one for each player, that are each best responses against one another.

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*.

A Beautiful Mind

Next Time: More Game TheoryIterated Prisoners Dilemma

Try 6.1, 6.3, 6.5

EC4004 Lecture 6

Probability and Game TheoryDr Stephen Kinsella