{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Macroeconomics Exam Review 189

Macroeconomics Exam Review 189 - c 2001 Michael Carter All...

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

View Full Document Right Arrow Icon
3.256 By the Minimax theorem, every finite two person zero-sum game has a value. The previous result shows that this is attained at a Nash equilibrium. 3.257 If player 2 adopts the strategy 𝑡 1 𝑓 p ( 𝑡 1 ) = 𝑝 1 + 2 𝑝 2 < 0 if 𝑝 1 > 2 𝑝 2 If player 2 adopts the strategy 𝑡 5 𝑓 p ( 𝑡 5 ) = 𝑝 1 2 𝑝 2 < 0 if 𝑝 1 < 2 𝑝 2 Therefore 𝑣 1 ( p ) = min 𝑧 𝑍 𝑓 p ( z ) min { 𝑓 p ( 𝑡 1 ) , 𝑓 p ( 𝑡 5 ) } < 0 for every p such that 𝑝 1 = 𝑝 2 . Since 𝑝 1 + 𝑝 2 = 1, we conclude that 𝑣 1 ( p ) { = 0 p = p = ( 2 / 3 , 1 / 3 ) < 0 otherwise We conclude that 𝑣 1 = max p 𝑣 1 ( p ) = 0 which is attained at p = ( 2 / 3 , 1 / 3 ). 3.258 1. 𝑣 2 = min z 𝑍 𝑚 max 𝑖 =1 𝑧 𝑖 Since 𝑍 is compact, 𝑣 2 = 0 implies there exists ¯ z 𝑍 such that 𝑚 max 𝑖 =1 ¯ 𝑧 𝑖 = 0 which implies that ¯ z 0. Consequently 𝑍 ∩ ℜ 𝑛 = . 2. Assume to the contrary that there exists
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