Homework Help is Here – Start Your Trial Now!
Business
Economics
an auditor and a taxpayer play the following strategic game. The auditor must choose hether to Audit (A) the taxpayer or not (N). The taxpayer independently decides whether o be Honest (H) in reporting her income or to Cheat (C). Since auditing is costly, the uditor prefers not to audit the taxpayer if she reports honestly, but prefers to audit if the axpayer cheats. If the taxpayer is caught cheating (i.e. if she cheats and is audited), then he receives a severe punishment. If she is not caught, she prefers cheating to being honest. uppose that payoffs are as in the following matrix: Auditor Taxpayer C H A 2,0 4,-10 N 4,0 0,4 (a) Find all (mixed strategy) Nash equilibria of this game.

an auditor and a taxpayer play the following strategic game. The auditor must choose hether to Audit (A) the taxpayer or not (N). The taxpayer independently decides whether o be Honest (H) in reporting her income or to Cheat (C). Since auditing is costly, the uditor prefers not to audit the taxpayer if she reports honestly, but prefers to audit if the axpayer cheats. If the taxpayer is caught cheating (i.e. if she cheats and is audited), then he receives a severe punishment. If she is not caught, she prefers cheating to being honest. uppose that payoffs are as in the following matrix: Auditor Taxpayer C H A 2,0 4,-10 N 4,0 0,4 (a) Find all (mixed strategy) Nash equilibria of this game.

Managerial Economics: A Problem Solving Approach
Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter18: Auctions
Section: Chapter Questions
Problem 18.1IP
See similar textbooks
icon
Related questions
Question
An auditor and a taxpayer play the following strategic game. The auditor must choose whether to Audit (A) the taxpayer or not (N). The taxpayer independently decides whether to be Honest (H) in reporting her income or to Cheat (C). Since auditing is costly, the auditor prefers not to audit the taxpayer if she reports honestly, but prefers to audit if the axpayer cheats. If the taxpayer is caught cheating (i.e. if she cheats and is audited), then she receives a severe punishment. If she is not caught, she prefers cheating to being honest. Suppose that payoffs are as in the following matrix: Auditor Taxpayer C 4, -10 0,4 H A 2,0 N 4,0 (a) Find all (mixed strategy) Nash equilibria of this game. Solution: There is no NE in pure strategies. Moreover, since each pure strategy has a unique best response, there is no NE in which either player plays a pure strategy. If the Auditor chooses A with probability p and the Taxpayer chooses H with probability q, then the condition for the Auditor to be indifferent between A and N is 2q + 4(1 — q) = 4q, and therefore q = 3. The indifference condition for the Taxpayer is 0= -10p+4(1-p), and therefore p = . Thus there is only one NE, which is given by (p, q) = (1, 3). -
Transcribed Image Text:An auditor and a taxpayer play the following strategic game. The auditor must choose whether to Audit (A) the taxpayer or not (N). The taxpayer independently decides whether to be Honest (H) in reporting her income or to Cheat (C). Since auditing is costly, the auditor prefers not to audit the taxpayer if she reports honestly, but prefers to audit if the axpayer cheats. If the taxpayer is caught cheating (i.e. if she cheats and is audited), then she receives a severe punishment. If she is not caught, she prefers cheating to being honest. Suppose that payoffs are as in the following matrix: Auditor Taxpayer C 4, -10 0,4 H A 2,0 N 4,0 (a) Find all (mixed strategy) Nash equilibria of this game. Solution: There is no NE in pure strategies. Moreover, since each pure strategy has a unique best response, there is no NE in which either player plays a pure strategy. If the Auditor chooses A with probability p and the Taxpayer chooses H with probability q, then the condition for the Auditor to be indifferent between A and N is 2q + 4(1 — q) = 4q, and therefore q = 3. The indifference condition for the Taxpayer is 0= -10p+4(1-p), and therefore p = . Thus there is only one NE, which is given by (p, q) = (1, 3). -
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Bayesian Nash Equilibrium
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Managerial Economics: A Problem Solving Approach
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Microeconomic Theory
Microeconomic Theory
Economics
ISBN:
9781337517942
Author:
NICHOLSON
Publisher:
Cengage
Principles of Economics 2e
Principles of Economics 2e
Economics
ISBN:
9781947172364
Author:
Steven A. Greenlaw; David Shapiro
Publisher:
OpenStax
Essentials of Economics (MindTap Course List)
Essentials of Economics (MindTap Course List)
Economics
ISBN:
9781337091992
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Brief Principles of Macroeconomics (MindTap Cours…
Brief Principles of Macroeconomics (MindTap Cours…
Economics
ISBN:
9781337091985
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Principles of Economics (MindTap Course List)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS