Assoc. Prof. Yeşim Kuştepeli1 GAME THEORY AND APPLICATIONS UNCERTAINTY AND EXPECTED UTILITY.

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Assoc. Prof. Yeşim Kuştepeli1 GAME THEORY AND APPLICATIONS UNCERTAINTY AND EXPECTED UTILITY

Assoc. Prof. Yeşim Kuştepeli2 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.

Assoc. Prof. Yeşim Kuştepeli3 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.

Assoc. Prof. Yeşim Kuştepeli4 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) b) state of the world: dry (probability: %40) 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)

Assoc. Prof. Yeşim Kuştepeli5 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) Expected payoff matrix

Assoc. Prof. Yeşim Kuştepeli6 2. Exogenous Uncertainty in dynamic Games 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

Assoc. Prof. Yeşim Kuştepeli7 Macrosoft’s profits with 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 600 Net profit

Assoc. Prof. Yeşim Kuştepeli8 Microcorp’s profits if it enters the market 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

Assoc. Prof. Yeşim Kuştepeli9 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.

Assoc. Prof. Yeşim Kuştepeli10 Ex. Heads-tails game Player 2 Player 1 headsTails Heads(-1,1)(1,-1) tails(1,-1)(-1,1) No Nash equilibrium in pure strategies

Assoc. Prof. Yeşim Kuştepeli11 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.