041807 - Lecture Recall Finite strategic form games PSNE...

  • Notes
  • 501844684_ch
  • 4
  • 100% (3) 3 out of 3 people found this document helpful

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

Lecture ??: 04/18/2007 Recall: Finite strategic form games, PSNE, mixed strategies, Nash equilibrium with possibly mixed strategies, examples. Recall definition of Nash equilibrium : A (possibly mixed) strateg profile (σ 1 * , σ 2 * , …, σ n * )= σ * is a NE for every I and every mixed stratigey σ i є Ai , the following holds: u i 1 * ,…, σ i-1 * , σ i * , σ I+1 * ,…, σ n * )>=u i ( ie. σ i * is a best reply or best response for player i to the “opposition strategy profile” σ -i * = (σ 1 * , σ 2 * ,…, σ i-1 * , σ i+1 * ,…, σ n * ) ie. “σ * is a NE” just means “For all I, σ i * is a best rply to the opposition choices in σ * Defintion: Given σ i є Ai , the support of σ i (supp(σ i )) is the set of pure actions in A i to which σ i assigns positive probability. Fact: If σ * is a NE, then, for every I, every action in supp(σ i * ) is a best reply to the opposition strategy profile (σ 1 * ,…, σ i-1 * , σ i+1 * ,…, σ n * ) (Nb.: actions in A i <--> strategies in Ai assigning all probabilities to one action) Idea of proof: u i * )=a convex combination of terms of the form u i 1 * ,…, σ i-1 * , a i * , σ I+1 * ,…, σ n * ) where a i is a member of supp(σ i * ). If any such a i is not a best reply to σ- i *
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