Lecture 26 - Political Science C135 Economics C110...

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Political Science C135 Economics C110 Professor Robert Powell 11/30/10 Lecture 26 ASUC Lecture Notes Online is the only authorized note-taking service at UC Berkeley. Do not share, copy, or illegally distribute (electronically or otherwise) these notes. Our student-run, non-profit program depends on your individual subscription for its continued existence. These notes are copyrighted by the University of California and are for your personal use only. DO NOT COPY Sharing or copying these notes is illegal and could end note taking for this course. ANNOUNCEMENTS Homework is due Thursday. We have one more topic to cover, intuitive criteria, but mostly I will use Thursday as a review session like we did before the midterm. After my review, I’ll open it up for questions. That’s the rest of the semester. LECTURE We’ve been learning in the context of signaling games. Last time we looked for Perfect Bayesian Equilibrium. These are more powerful than Subgame Perfect Equilibrium . In SPE, you insist that everyone plays NE. In PBE, you insist they play sensibly at each and every information set. Sensibility entails that given beliefs about every information set, you have to choose the action that maximizes your payoff. In the context of a signaling game, PBE requires that: 1. The sender has to behave sensibly, sending the message that maximizes its payoff given the receiver’s strategy. 2. The receiver has to behave optimally, but what we mean by this it that he has to take the course of action that maximizes his payoffs given his beliefs, which can be updated based on the signal of the sender. 3. Beliefs are compatible with the sender’s strategies. This compatibility exists in a separating equilibrium, where each type does something different, and the receiver believes that an action undoubtedly identifies one type, and the opposite action undoubtedly identifies the other type. In the game we ended with last time, this was the separating equilibrium, and you couldn’t separate the other way: You can also have a compatibility through pooling equilibrium. This is when a receiver’s beliefs are unchanged when they see a signal. There are only two possibilities. We can pool on an expensive campaign or we can pool on a cheap campaign. We’ll start with expensive. If they’re both supposed to take the same action, the receiver’s beliefs remain unchanged so the updated beliefs of probabilities are still .4 for S and .6 for M. The payoffs to R going yes and no are:
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PS C135 / ECON C110 ASUC Lecture Notes Online: Approved by the UC Board of Regents 11/30/10 DO NOT COPY Sharing or copying these notes is illegal and could end note taking for this course. 2 Y 1(.4)+0(.6)=.4 N 0(.4)+1(.6)=.6 Given these beliefs, she wants to vote no. An easy trick question on the final would be me handing you this asking if it’s a PBE. This is a “no, because an equilibrium has to have a set a strategies, and here we can’t have an equilibrium because we don’t know what R is doing after a signal of cheap on the
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Lecture 26 - Political Science C135 Economics C110...

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