# ECON 100B Study Guide - Midterm Guide: Grim Trigger, Subgame Perfect Equilibrium, Root Mean SquareExam

by OC2540294

Department

EconomicsCourse Code

ECON 100BProfessor

AllStudy Guide

MidtermThis

**preview**shows page 1. to view the full**5 pages of the document.**University of California, Irvine

Econ 100B Intermediate Economics

Mid-Term Test

Instructor: Jean-Paul Carvalho

Thurs 5 February 2015

Please print legibly

Name:

Student ID number:

Candidates should answer all questions in the space provided. You may con-

tinue on the back of the sheet if you need additional space. This is a closed-

book, closed-notes exam, with NO calculators.

The paper consists of 4 questions. The total number of points for the paper is 40.

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Q1. Consider the following game. A spy (row player) is trying to get away from the

villain (column player) by skiing down one of three routes. The villain can choose to

explode a bomb (which is costly) and cause an avalanche or not explode a bomb. Payoﬀs

are given by the following matrix:

Don’t Explode Explode

1 12,0 0,6

2 7,1 1,5

3 9,3 6,0

a. Are there any routes that the spy should never to choose? (2 marks)

b. Let qbe the probability with which the villain chooses ‘Don’t Explode’. What should

the spy do if q > 2

3? What about if q < 2

3? (3 marks)

c. Derive the mixed strategy Nash equilibrium of this game. Prove that it is an equilib-

rium. (5 marks)

(Remember to show all working)

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