{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

stat155hw4soln - Stat 155 Fall 2009 Solutions to Homework...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Stat 155 Fall 2009: Solutions to Homework 3 (was due October 1, 2009) 1. The payoff matrix is shown below, with player I’s choices along the rows, and player II’s choices along the columns. Black Red Black 1 - 2 Red - 7 8 Using equalizing strategies, as discussed in class, we will solve for the optimal p to find the value of the game where p is the probability that Player I chooses the Black Ace, and 1 - p is the probability that Player I chooses the Red 8. Equating Player I’s expected payoffs under the two cases of Player II playing Black or Red, we get: 1 · p - 7(1 - p ) = - 2 p + 8(1 - p ) We solve this to get p = 5 / 6. This gives the value of the game to be - 1 / 3. If Player II’s optimal strategy is ( q, 1 - q ), where q is the probability that Player II chooses Black, then we can use the same method to solve for q , getting q = 5 / 9. Thus, Player I’s optimal strategy: (5 / 6 , 1 / 6), Player II’s optimal strategy: (5 / 9 , 4 / 9), and Value of the game = - 1 / 3. 2. Payoff matrix: Rock Paper Scissors Rock 0 - 1 1 Paper
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern