uncertainty and expected utility prof. dr. yeşim kuştepeli eco 4413 game theory 1
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UNCERTAINTY AND EXPECTED UTILITY
Pro
f. Dr. Y
eşim
Kuşte
peli E
CO
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Gam
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heory1
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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Pro
f. Dr. Y
eşim
Kuşte
peli E
CO
44
13
Gam
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Theory