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UNCERTAINTY AND EXPECTED UTILITY

UNCERTAINTY AND EXPECTED UTILITY.

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UNCERTAINTY AND EXPECTED UTILITY

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

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

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

  4. Ex. Oil drilling game a) state of the world : gusher (probability: %60) b) state of the world: dry (probability: %40) Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory

  5. Expected payoff matrix Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory

  6. 2. Exogenous Uncertainty in dynamic Games • Ex. Software game • Macrosoft’s profits with no competitor Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory

  7. Macrosoft’s profits with competitor Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory

  8. Microcorp’s profits if it enters the market Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory

  9. 3) Endogenous Uncertainty in Static Games • A pure strategyis 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. Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory

  10. Ex. Heads-tails game Prof. Dr. Yeşim Kuştepeli ECO 4413 Game Theory No Nash equilibrium in pure strategies

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

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