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Unformatted text preview: Lecture I-II: Motivation and Decision Theory Markus M. Mobius February 7, 2004 1 Two Motivating Experiments Experiment 1 Each of you (the students in this course) have to declare an integer between 0 and 100 to guess 2/3 of the average of all the responses. More precisely, each student who guesses the highest integer which is not higher than 2/3 of the average of all responses, will receive a prize of 10 Dollars. How should you play this game? A naive guess would be that other players choose randomly a strategy. In that case the mean in the game would be around 50 and you should choose 33. But you realize that other players make the same calculation - so nobody should say a number higher than 33. That means that you should not name a number greater than 22 - and so on. The winning number was 13. That means that people did this iteration about 3 times. But in fact, the stated numbers were all over the place - ranging from 0 to 40. That means that different students had different estimates of what their fellow students would do. Being aware of your fellow players existence and trying to anticipate their moves is called strategic behavior. Game theory is mainly about designing models of strategic behavior. In this game, the winner has to correctly guess how often his fellow players iterate. Assuming infinite iterations would be consistent but those who bid 0 typically lose badly. Guessing higher numbers can mean two things: (a) the player does not understand strategic behavior or (b) the player understands strategic behavior but has low confidence 1 in the ability of other players to understand that this is a strategic game. Interestingly, most people knew at least one other person in the class (hence there was at least some degree of what a game theorist would call common knowledge of rationality). 1 Experiment 2 I am going to auction a textbook (Osbornes book). It costs about 60 Dollars on Amazon. Each of your can bid secretly on the book and the highest bidder wins the auction. However, all of you have to pay your bid regardless of whether you win or lose. In this game there is no optimal single bid for all players. You can check that for all cases where each player i bids some fixed bid b i at least one of the players will regret her decision and try to reverse it - we say that there is no pure strategy Nash equilibrium in this game. Consider for example the case where all player bid 55 Dollars. Then some player should bid 55 and 5 cents. No equilibrium! There is an equilibrium if we allow players to randomize. You can check that with two players who pick random numbers between 0 and 60 with equal probability no player would want to change her pick - all picks will give her zero profit in expectation....
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This note was uploaded on 05/19/2010 for the course DFDAS 220 taught by Professor Ding during the Fall '10 term at Academy of Art University.
- Fall '10