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Unformatted text preview: Econ106G Lecture Note 1 Hong Feng Jun 24, 2008 1 Class Games 1. Second-Price Auction There are six envelopes, with one check in each. The amounts of the checks are 1, 2, 4, 8, 16 and 32 dollars. You will bid on a chance to randomly choose one of the six envelopes and take the check in it. First write down you valuation, which means you the maximum amount of money you will pay for this "chance to choose". Then submit your bid. The student with the highest bid will win the chance, and he needs to pay the second highest bid. If more than one students submit the highest bid, then one of them will be randomly chosen as the winner, and he will pay the highest bid (because now the second highest bid equals to the highest bid). 2. 2/3 Game Each student need to write down an integer between 0 and 100. Then 2/3 of the highest number will be calculated. Let&s call it "number 2/3". The student whose number is closest to but smaller than "number 2/3" is the winner. He& ll get $5. Those students whose numbers are higher than "number 2/3" will be punished: each week one of them will be chosen to help me clean the blackboard after class. 2 What is Game Theory? De&nition 1 Game theory is a mathmatical tool to analyze situations in which two or more rational agents strategically make decisions that will in&uence one anothers welfare. Its also called "Interactive Decision Theory" Key terms in this denition: & Interaction: In a game theory model, there must be at least two agents, and each agent&s decision will inuence not only himself, but also other agents& welfare. Compare this to "Decision Theory", where everyone&s decision only aects his own welfare. A good example is that when you go to a restaurant with your friends, if everybody pays for their own food, it&s simply a "decision theory" model. But if you agree to split the bill evenly within the group, then we need game theory to study the situation.evenly within the group, then we need game theory to study the situation....
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