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Unformatted text preview: Econ 171 Spring 2010 Notes for Lecture 2 April 1 Note: we will begin class by playing some in-class games and by continuing to go through the “Handout on Normal Form Games” Overview In these notes we will continue looking at games in the normal (or strategic) form, which is a model in which each player chooses her action once and for all, with the choices being made simultaneously. We have three goals: • The first section aims to shore up your understanding of Iterated Elimination of Domi- nated Strategies (or Iterated Dominance for short), particularly when it involves mixed strategies. • The second section seeks to familiarize you with several classical normal form games and the issues that they highlight. • The third section seeks to familiarize you with iterated dominance in normal form games by presenting an application to supplement those presented in Chapter 8 of Watson. Review of Important Terms and Concepts We begin by returning to the Handout on Normal Form Games. First, recall game a), oth- erwise known as the Prisoners’ Dilemma. We solved this game by applying the concept of dominance, which relies on the assumption that the players are rational. Player 1 Player 2 C D C 2 , 2 , 3 D 3 , 1 , 1 a) Figure 1: Prisoners’ Dilemma Next, recall game b). Applying dominance alone did not yield a unique prediction, but iterated elimination of dominated strategies, or iterated dominance did. In general, games for which iterated dominance provides a unique prediction are called dominance solvable . In this class of games, iterated dominance is equivalent to another solution concept called rationalizability , which uses the assumption that rationality is common knowledge. We call the strategies that survive this concept rationalizable . 1 In class, we did not get to game c). If you have not already done so, please try to find the set of rationalizable strategies in this game before reading on. X Y A 4 , 1 2 , B 3 , 2 1 , 5 C 1 , 2 4 , b) X Y A 3 , 4 , 2 B 4 , 2 1 , 1 C , 2 , 3 c) We begin by noting that A is dominated by B . Whether Player 1 believes 2 will play X or Y , she is better off playing B . Thus we can eliminate A . However, we cannot eliminate any further strategies. B is a best response to the belief that 2 will play X and C is a best response if 2 plays Y . Likewise, for Player 2 X is a best response to B and Y is a best response to C . Thus, none of the remaining strategies are dominated. This game shows that iterated dominance does not always yield a unique prediction, i.e. not all games are dominance solvable. Now lets look at game d), through which we kind of rushed in class. First, we’ll use this game to clarify some important terms. What is a difference between a strategy, strategy space, strategy profile, and an outcome? A strategy is a plan for one player, e.g. B is a strategy for Player 1 and X is a strategy for Player 2. A strategy profile is a vector of strate- gies, one for each player, e.g. ( B,X ). A player’s)....
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- Fall '08
- Game Theory, player