Problem 1? 228 CHAPIER T Game Theory 8,1 3,2 0D Figure T10 Problem I ci C2 C3 C4
ID: 1151604 • Letter: P
Question
Problem 1?
228 CHAPIER T Game Theory 8,1 3,2 0D Figure T10 Problem I ci C2 C3 C4 R2 6,5 2,3 5, 1 7, 4 Figurc T.11 Problem 3 4. Explain the relationship between the Prisoners' Dilemma and the arms race during the cold war 5. In the UnitolSullesseveral states have allrnlid looutlaw plea bargains Abe ollerora reduced senience in restum for a guilty plea. Advocates argue that faimess requires a given crime to receiwe the sarne punishment, whoever comunits it and regardless of other circumstances. What effect do you think that such hans on plea hargaining will have on criminal law enforcement Problemns I. lind the Nash equilibrium to the gane in Figure 7.10 2. Find the mixed strategy equilibrium to the Battle of the Sexes game in ligure 7.7 , Coriskler the game in Figure 1 Using iterative eliminainn o liever best resp oses, lind the set of rationalizable strategies. Find the Nash equilibriun. 1. A planning conmitlee with three members, A, B, and C is trying to decide whether or not to propose two new projects for the cily, a libary and a movie theater Each memher feels that the requingd increase in taxes woulkd create a disutiliy of 10, the theater would generate a bencit of 40 for A, while the library woukl generate a benelit of 40 for B, Cis nol imternsted in either oplion. A majg rity vole will deturnine which, if any, projects should te proposwd, Since does nol value the library or the theater, it would newer be a rationalizable stralegyExplanation / Answer
Ans) nash equilibrium is (M,M) i.e (4,4) when row and column both choose M
When row chooses U, Column chooses R because it gets higher pay off i.e 8
When row chooses M, Column chooses M because it gets higher pay off i.e 4
When row chooses D, Column chooses M because it gets higher pay off i.e 2
When column chooses L, row chooses D because it gets higher pay off i.e 8
When Column chooses M, row chooses M because it gets a higher payoff i.e 4
When column chooses R, row chooses M because it gets a higher payoff i.e 2