167shw1 - Game Theory Steven Heilman Please provide...

Info icon This preview shows pages 1–2. Sign up to view the full content.

Game Theory Steven Heilman Please provide complete and well-written solutions to the following exercises. Due April 5, in the discussion section. Homework 1 Exercise 1. Let n be a positive integer. Consider the game Chomp played on an n × n board. Explicitly describe the winning strategy for the first player. (Hint: the first move should remove the square which is diagonally adjacent to the lower left corner.) Exercise 2. Compute the following nim-sums: 3 4, 5 9. Then, let a, b, c be nonnegative integers. Prove that a a = 0 and ( a b ) 0 = a b . Exercise 3. Consider the nim position (9 , 10 , 11 , 12). Which player has a winning strategy from this position, the next player or the previous player? Describe a winning first move. Exercise 4. Consider the game of Chomp played on a board of size 2 × ∞ . Recall that a typical Chomp game board is n × m , so that the board has n rows and m columns. We can label the rows as { 1 , 2 , . . . , n } and we can label the columns as { 1 , 2 , . . . , m } , where n, m are positive integers. On a 2 × ∞
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Image of page 2
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