UNCERTAINTY AND EXPECTED UTILITY

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If all players know with certainty the outcome of any strategy profile, the game is deterministic.

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.

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1) EXOGENOUS UNCERTAINTY IN STATIC GAMES

All 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.

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Ex. Oil drilling game

a) state of the world : gusher (probability: %60)

player2

Dont drill narrow wide

Pl. 1 Dont drill (0,0) (0,44) (0,31)

Narrow (44,0) (14,14) (-1,16)

wide (31,0) (16,-1) (1,1)

player2

Dont drill narrow wide

Pl. 1 Dont drill (0,0) (0,-16) (0,-29)

Narrow (-16,0) (-16,-16) (-16,-29)

wide (-29,0) (-29,-16) (-29,-29)

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b) state of the world: dry (probability: %40)

player2

Dont drill narrow wide

Pl. 1 Dont drill (0,0) (0,20) (0,7)

Narrow (20,0) (2,2) (-7,-2)

wide (7,0) (-2,-7) (-11,-11)

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Expected payoff matrix

2. EXOGENOUS UNCERTAİNTY İN DYNAMİC GAMES

Ex. Software game

Macrosoft’s profits with no competitor

Slick campaign Simple campaign

High demand( % 50)

Low demand( % 50)

High demand( % 50)

Low demand( % 50)

Profit in year 1

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

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Slick campaign Simple campaign

High demand( % 50)

Low demand( % 50)

High demand( % 50)

Low demand( % 50)

Profit in year 1

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

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•Macrosoft’s profits with competitor

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Slick campaign Simple campaign

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 cost

300 300 300 300

Net profit 50 -200 300 -100

Microcorp’s profits if it enters the market

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 2

Player 1

heads Tails

Heads (-1,1) (1,-1)

tails (1,-1) (-1,1)

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No Nash equilibrium in pure strategies

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

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.

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