UNCERTAINTY AND EXPECTED UTILITY Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory 1.

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UNCERTAINTY AND EXPECTED UTILITY Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory 1

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. 2 Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory

1) E XOGENOUS U NCERTAINTY IN STATIC G AMES 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. 3 Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory

Ex. Oil drilling game a) state of the world : gusher (probability: %60) player2 Dont drillnarrowwide Pl. 1Dont drill(0,0)(0,44)(0,31) Narrow(44,0)(14,14)(-1,16) wide(31,0)(16,-1)(1,1) player2 Dont drillnarrowwide Pl. 1Dont drill(0,0)(0,-16)(0,-29) Narrow(-16,0)(-16,-16)(-16,-29) wide(-29,0)(-29,-16)(-29,-29) Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory 4 b) state of the world: dry (probability: %40)

player2 Dont drillnarrowwide Pl. 1Dont drill(0,0)(0,20)(0,7) Narrow(20,0)(2,2)(-7,-2) wide(7,0)(-2,-7)(-11,-11) Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory 5 Expected payoff matrix

2. E XOGENOUS U NCERTAINTY IN DYNAMIC G AMES Ex. Software game Macrosoft’s profits with no competitor Slick campaignSimple campaign High demand ( % 50) Low demand ( % 50) High demand ( % 50) Low demand ( % 50) Profit in year Profit in year Total profit Advertisement cost Net profit Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory 6

Slick campaignSimple campaign High demand ( % 50) Low demand ( % 50) High demand ( % 50) Low demand ( % 50) Profit in year Profit in year Total profit Advertisement cost 600 Net profit Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory 7 Macrosoft’s profits with competitor

Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory 8 Slick campaignSimple campaign High demand ( % 50) Low demand ( % 50) High demand ( % 50) Low demand ( % 50) Profit in year Profit in year Total profit Advertisement cost 300 Net profit 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. 9 Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory

Ex. Heads-tails game Player 2 Player 1 headsTails Heads(-1,1)(1,-1) tails(1,-1)(-1,1) Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory 10 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. 11 Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory