Simultaneous Games - Mixed Strategies II.pdf - Simultaneous Games Mixed Strategies II Mixed-Strategy Nash Equilibrium ZERO-SUM GAME KICKER Left(pL

# Simultaneous Games - Mixed Strategies II.pdf - Simultaneous...

• 5

This preview shows page 1 - 2 out of 5 pages.

Simultaneous Games - Mixed Strategies II Mixed-Strategy Nash Equilibrium GOALIE Left ( q L ) Center Right ( q R ) KICKER Left ( p L ) 45 90 90 Center 85 0 85 Right ( p R ) 95 95 60 Figure 7.10 Penalty Kick Does the game have a Nash equilibrium in pure strategies? How does a mixed-strategy Nash equilibrium look like? Can the MSNE involve only two pure strategies? ... when you have eliminated the impossible, whatever remains, however improbable, must be truth. Sir Arthur Conan Doyle (Sherlock Holmes) 1. W/o Kicking Right (i.e. p R = 0) Goalie: Right’s expected probability = 90 p L +85(1 - p L ) > Left’s or Center’s expected probability Goalie will stop guessing Right But Kicker will kick Right ⇒⇐ 2. W/o Kicking Center (i.e. 1 - p L - p R = 0) Goalie: Center’s expected probability = 90 p L + 95 p R > Left’s or Right’s expected probability Goalie will stop guessing Center Kicker: Mixing Left and Right 45 q L + 90 q R = 95 q L + 60 q R (= 73 . 125, using q L + q R = 1) But Kicker will kick Center ⇒⇐ 3. W/o Kicking Left (i.e. p L = 0) Goalie: Left’s expected probability = 85(1 - p R ) + 95 p R > Cen- ter’s or Right’s expected probability Goalie will stop guessing Left 1 probability to goal (45,90,90) ZERO-SUM GAME

Subscribe to view the full document.

• Fall '16

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes