# 12_6 - Pic 1 An alternative way of thinking about Nash...

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

Pic 1: An alternative way of thinking about Nash equilibria in two- player Pic2: example: The game in Tables 28.2&29.1 Column Left Right Row Top 2,1 0,0 Bottom 0,0 1,2 For a two-player game: Suppose you are one of the players For any choice that the other player can make, a choice that maximizes your payoff (given the other player’s choice) is called a “best response” or best reply A Nash Equilibrium is a pair of strategies which are mutually consistent (in the sense that each player’s strategy is a best reply to the other player’s strategy) Best responses for row: - If column chooses Left. Row’s best response is Top - If Column chooses Right, row’s best response is Bottom Best response for Column: - If row chooses Top, Column’s best response is Left - If row chooses bottom, Column’s best response is right (top, left) is mutually consistent - if row thinks column will play left, row wants to play top - if column thinks row will play top, column wants to play left - (top, left) is a Nash Equilibrium (Bottom, Right) is mutually consistent - If row thinks column will play right, row wants to play bottom, - if column thinks row will play bottom, column wants to play right - (bottom, right) is a Nash Equilibrium When there is always a unique best response: - -For each choice r that row can make, let (r) =column’s best response to row’s choice r - For each choice c that column can make, let ( c) = row’s best response to column’s choice c - A Nash Equilibrium is a pair of strategies (r*, c*) such that C*= (r*) r*= (c*) For the game in Table 28.2&29.1 -

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### 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