Prof. Dr. Yeşim Kuştepeli
ECO 4413 Game Theory
UNCERTAINTY AND
EXPECTED UTILITY
1
 If
Prof. Dr. Yeşim Kuştepeli
all players know with certainty the
outcome of any strategy profile, the game is
deterministic.
ECO 4413 Game Theory
The expected utility hypothesis implies that
for each player in a game, each outcome of
the game can be assigned a number such
that the player acts as if he is maximizing
his expected utility.
2
1) EXOGENOUS UNCERTAINTY IN STATIC GAMES
the factors that affect the outcome of the
game but are not under any player’s control
are called “the state of the world”.
 The state of the world is unpredictable or
random.
 Nature is indifferent to the outcomes and
selects the state of the world randomly
according to fixed probabilities.
Prof. Dr. Yeşim Kuştepeli
 All
ECO 4413 Game Theory
3

Ex. Oil drilling game
a) state of the world : gusher (probability: %60)
player2
narrow
wide
Dont drill
(0,0)
(0,44)
(0,31)
Narrow
(44,0)
(14,14)
(-1,16)
wide
(31,0)
(16,-1)
(1,1)
Prof. Dr. Yeşim Kuştepeli
Pl. 1
Dont drill
ECO 4413 Game Theory
b) state of the world: dry (probability: %40)
player2
Pl. 1
Dont drill
narrow
wide
Dont drill
(0,0)
(0,-16)
(0,-29)
Narrow
(-16,0)
(-16,-16)
(-16,-29)
wide
(-29,0)
(-29,-16)
(-29,-29)
4
Expected payoff matrix
player2
wide
Dont drill
(0,0)
(0,20)
(0,7)
Narrow
(20,0)
(2,2)
(-7,-2)
wide
(7,0)
(-2,-7)
(-11,-11)
ECO 4413 Game Theory
narrow
Prof. Dr. Yeşim Kuştepeli
Pl. 1
Dont drill
5
2. EXOGENOUS UNCERTAINTY IN DYNAMIC GAMES

Macrosoft’s profits with no competitor
Simple campaign
High
demand
( % 50)
Low
demand
( % 50)
High demand
( % 50)
Low demand
( % 50)
900
600
200
200
Profit in year 2 700
200
1200
400
Total profit
1600
800
1400
600
Advertisement
cost
600
600
200
200
Net profit
1000
200
1200
400
Profit in year 1
ECO 4413 Game Theory
Slick campaign
Prof. Dr. Yeşim Kuştepeli

Ex. Software game
6
•Macrosoft’s profits with competitor
High
demand
( % 50)
Low
demand
( % 50)
High demand
( % 50)
Low demand
( % 50)
900
600
200
200
Profit in year 2 350
100
600
200
Total profit
1250
600
800
400
Advertisement
cost
600
600
600
600
Net profit
650
0
600
200
Profit in year 1
ECO 4413 Game Theory
Simple campaign
Prof. Dr. Yeşim Kuştepeli
Slick campaign
7
Microcorp’s profits if it enters the market
High
demand
( % 50)
Low
demand
( % 50)
High
demand
( % 50)
Low demand
( % 50)
Profit in year 1 0
0
0
0
Profit in year
2
350
100
600
200
Total profit
350
100
600
200
Advertisement 300
cost
300
300
300
Net profit
-200
300
-100
50
ECO 4413 Game Theory
Simple campaign
Prof. Dr. Yeşim Kuştepeli
Slick campaign
8
Prof. Dr. Yeşim Kuştepeli
ECO 4413 Game Theory
3) Endogenous Uncertainty in Static Games
 A pure strategy is one that calls for the selection of
exactly one action at one decision node.
 Many simultaneous move games do not have a
Nash equilibrium if the players are restricted to
pure strategies.
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Ex. Heads-tails game
Player
1
Tails
Heads
(-1,1)
(1,-1)
tails
(1,-1)
(-1,1)
No Nash equilibrium in pure strategies
ECO 4413 Game Theory
heads
Prof. Dr. Yeşim Kuştepeli
Player 2
10

ECO 4413 Game Theory
When more than one player adopts a mixed
strategy, these players randomize
independently of each other. Independence
means that knowledge of strategy chosen by
one player provides no new information
about the strategy that will be chosen by
any other player who has adopted a mixed
strategy.
Prof. Dr. Yeşim Kuştepeli

If there are no pure strategy Nash
equilibrium, it is possible to expand the set
of possible strategies and allow players to
choose among their actions randomly=
Mixed strategy
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