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Presented by: Zhenhuan Sui Nov. 24 th, 2009

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Game Theory: applied mathematics in social sciences, especially economics. It is to mathematically find behaviors in strategic situations in which an individual person's successful choices depend on the choices of others. It tries to find the equilibriums in the games in which each player uses a strategy that they are unlikely to change. Daily examples: poker, chess

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Modern Game Theory is started by Zermelo, Borel and von Neumann Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern, 1944 Developed extensively in the 1950s John Forbes Nash Jr, Nash equilibrium, game theorists have won Nobel prizes in economics

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Players: people who can make choices ( two and multiple) Strategies: a completed plan or scheme of activities in the whole game (finite and infinite) Payoffs: results; function of the strategies of all players (payoff function) Orders: order of players to make choices; different order→different game Equilibrium: in supply-demand relationship, under a certain price of a commodity in the market, all the customers can get it by this price and all the sellers can sell it at this price.

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For two or more than two players in a game in which each player knows the equilibrium strategies of the other players, and no player has anything to gain by changing only his or her own strategy unilaterally while others keep unchanged, the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium. It is a stable/unchanged result in the game.

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Arms race: increase military expenditure(betray) or to make an agreement to reduce weapons (cooperate) Tariff: Increase (betray) or decrease to benefit the flow of goods (cooperate) Bicycle race: Tour de France; in peloton for most of the time to cost less energy; all do not want to lead at the beginning (betray each other); lead in turn( cooperate) ; one wants to lead all the way to the end( betray others); catch up in peloton( betray each other) ； final result will be that the one who betrays will win

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Cooperative or non-cooperative: cooperative if the players are able to achieve an agreement Symmetric and asymmetric: A symmetric game is a game where the payoffs of a particular strategy depend only on the other strategies employed, not on the identity of the players Discrete and continuous games: Continuous games allow players to choose a strategy from a continuous strategy set. Zero-sum and non-zero-sum: Zero-sum Game Theory is the situation in which one player's gain or loss balances or cancels with the losses or gains of the other player(s). The total gains of the players are added up, and the total losses are subtracted. The two results will sum to zero. Examples: Conservation of Happiness Mutual benefit (win-win) in economics Romance Love

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Situation: In a sty, there are one big and one small pig. At one end of the sty, there is a pedal. As long as one pig steps on it, some food will drop down at the other end of the sty. When the small pig steps the pedal, the big pig will finish all the food right before the small one arrives; when the big one steps the pedal, the small pig will finish half of the food when the big arrives and then they eat together. Result: the small pig will be the free rider waiting at the end with food and the big pig will run back and forth between the two ends. Analysis: The reason is that if the small pig steps the pedal, it will get nothing to eat, while it can get some food if it does not step. Therefore, it is a better choice to not step for small pig. Then the big pig knows that small pig will not step the pedal. So it has to step to get food.

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Decrease the dropping food to half: both pigs will not step the pedal Double the dropping food: society of communism, no sense of competition; (higher cost) Move the dropping-food position nearer to the pedal and decrease the dropping: the one work will finish the food and best stimulate the enthusiasm to work Stock market and companies

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Price decreasing race: harm to sellers(suicide), benefit to consumer. Ends by Nash equilibrium with zero profit (non-cooperative) Kids dividing one cake: one divides, one chooses Three people firing: the best one dies and worst one survive

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