EC4004
Lecture 6
Probability and Game Theory
Dr Stephen Kinsella

A Panda
is for life.
Not Just for
The Debs.

Today

1. Risk

2. Insurance

3. Game Theory

Yesterday

1. Risk

4 Ideas:

1.
Probability: Average
Frequency of events

2.
Expected value of game
with a number of
uncertain outcomes: size
of prize player will win
on average.

3.
Fair games are games that
cost precisely their
expected value.

4.
Risk aversion is tendency
for people to refuse to
accept fair games.

Combine 4 ideas with
Diminishing Marginal
Utility to get:

Utility
U
0 20 30 33 35 40 50 Income
(thousands
of euros)

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.

2. Insurance

Utility
U
U1
Income
0 20 25 35 (thousands
of euros)

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.

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 Theory
Iterated Prisoners Dilemma
Try 6.1, 6.3, 6.5

EC4004
Lecture 6
Probability and Game Theory
Dr Stephen Kinsella