lec1_17.pdf - Lecture 1 Intro to Game Theory Nash...

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Lecture 1: Intro to Game Theory + Nash Equilibrium 1 Quick Review: Individual Decision-Making Brief Overview: A game is just a way to model strategic interaction: the goal is come up with a simple representation (of the strategic situation) that captures the details that we think are relevant to agents°decisions, but omit irrelevant complicating details. The di/erence from your previous courses: in a strategic situation, your payo/ depends not only on your own decision, but also on the decisions taken by others. We will study various solution concepts, all based on common knowledge of full rationality: everyone (i) attempts to maximize his own payo/; (ii) everyone believes that everyone does this, and knows that everyone does this, and knows that everyone knows... 2 Examples 2.1 Example 1 There are 3 project options, {A,B,C}. Preferences for managers 1,2,3 (who must agree on a single choice) are as shown below: 1 : A ° B ° C 2 : B ° C ° A 3 : C ° A ° B You have probably seen in a previous course: there is no unanimous best choice, and not even a majority best choice; di¢ cult to even ±gure out which option should be chosen. But for strategic decision-making purposes: suppose that I, as the committee chairman, an- nounce the following decision rule: First, P1 announces his favorite. Then P2, and then P3 (all votes observed by all players). If there is a majority winner I pick it, otherwise I pick P2°s vote. What do we think will happen? What do we think should happen? Assume that all players know each others°preferences. Possible analysis (this uses the ²subgame perfect NE³solution concept, or SPNE): Suppose ±rst that in stage 1, P1 votes B: SPNE predicts that B will then be implemented, since a rational P2 can (and should) make sure that his favorite policy is implemented simply by also voting B.
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