class11_Game_

class11_Game_ - Econ 51, Winter 2011 Class #11 Midterm: we...

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1 Econ 51, Winter 2011 Class #11 Midterm: we should have grades for you by the next class. • PS #4 posted already • Today: Start game theory! Thursday, February 10, 2011
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2 Mid Quarter Evaluations Thanks for those who responded! Issues that came many times – The pace: mostly ok, too slow for some. – More examples in class. .. especially, examples related to real-world and PS: We will see more examples in the game theory part (i.e., from today) – PS difficult than class: to some extent it’s intentional. .. hope you benefit from study group (encouraged), TAs and sections. – Accent: Will try to improve (hope writing in slides helps. .. though it has its own cost). Feel free to ask. Please consider giving feedback to TAs as well. Thursday, February 10, 2011
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3 Game theory Thursday, February 10, 2011
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4 Game theory Game theory In everything we have done so far, each decision maker took the environment as given: Rob and Tom took prices as given (price-taking assumption) when deciding consumption. – Firms took prices as given and when deciding their production plan. These assumption make sense in many situations: for consumers who go for shopping, for small buyers and sellers in the stock market, and so forth. In many other situations, however, this is not such a great assumption (e.g., Bill Gates and Paul Allen negotiating on stock prices). Thursday, February 10, 2011
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5 Introduction Game theory Game Theory is the analysis of optimal decision making when there exists strategic interaction. Namely, we want to study what optimal behavior means once we know that what we do may affect what others would do, and vice versa. Recall the bridge construction for Rob and Tom: how could we analyze what agreement they would reach? We need tools to figure out how one’s decisions would affect the other’s. Thursday, February 10, 2011
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6 Overview Game theory •As mentioned later, applications of game theory appear in almost all fields of economics : industrial organization (games among firms), labor economics (a game between a worker and a firm, or between a husband and wife), macroeconomics (central banker vs. the public), and many others. •Today we will see simultaneous move (normal form) games. • Sequential move (extensive form) games later. •We will talk a lot about practical examples later (some today). Thursday, February 10, 2011
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Normal form (simultaneous move) games Game theory A normal form game consists of the following items: • A set of N players : i={1,2,. ..,N} A set of possible strategies for each player: S i ={s i1 ,s i2 ,...} for player i • A payoff (utility) function which tells us the payoffs each player gets as a result of the strategies played by all players : π i (s 1 ,s 2 ,...,s N ) Note: we often use instead the notation π i (s i ,s -i ) , where s -i denotes the strategies of all players but i . Thursday, February 10, 2011
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class11_Game_ - Econ 51, Winter 2011 Class #11 Midterm: we...

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