{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Section-6-Game-Theory-Dominant-Strategies-slides

# Section-6-Game-Theory-Dominant-Strategies-slides - Game...

This preview shows pages 1–9. Sign up to view the full content.

Game Theory: Dominant and Dominated Strategies Todd Sarver Northwestern University Econ 310-2 – Fall 2011 Todd Sarver (Northwestern University) Game Theory Econ 310-2 – Fall 2011 1 / 30

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

View Full Document
Outline 1 Components of a Game 2 Examples 3 Solution Concepts Dominant Strategies Iterated Elimination of Strictly Dominated Strategies 4 Non-Dominance Solvable Games 5 Pareto Efficiency Todd Sarver (Northwestern University) Game Theory Econ 310-2 – Fall 2011 2 / 30
Components of a Game Definition A Game consists of: 1 A set of players: 1 , . . . , n 2 A set of possible strategies for each player strategy = complete action plan specifying what the player will do in every possible scenario that could arise in the game. Denote a generic strategy for player i by s i 3 A payoff/utility function u i for each player i Player i ’s utility could depend on the strategies chosen by all players, not just her own strategy. That is, u i is a function of the strategy profile : s = ( s 1 , s 2 , . . . , s n ) . Todd Sarver (Northwestern University) Game Theory Econ 310-2 – Fall 2011 3 / 30

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

View Full Document
Components of a Game Definition A Game consists of: 1 A set of players: 1 , . . . , n 2 A set of possible strategies for each player strategy = complete action plan specifying what the player will do in every possible scenario that could arise in the game. Denote a generic strategy for player i by s i 3 A payoff/utility function u i for each player i Player i ’s utility could depend on the strategies chosen by all players, not just her own strategy. That is, u i is a function of the strategy profile : s = ( s 1 , s 2 , . . . , s n ) . Note: This is sometimes also called a Normal-Form Game . Todd Sarver (Northwestern University) Game Theory Econ 310-2 – Fall 2011 3 / 30
Illustration Consider a game with two players, 1 and 2. Suppose player 1 has two strategies: a, b (so s 1 = a or s 1 = b ) Suppose player 2 has three strategies: c, d, e (so s 2 = c , s 2 = d , or s 2 = e ) Todd Sarver (Northwestern University) Game Theory Econ 310-2 – Fall 2011 4 / 30

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

View Full Document
Illustration Consider a game with two players, 1 and 2. Suppose player 1 has two strategies: a, b (so s 1 = a or s 1 = b ) Suppose player 2 has three strategies: c, d, e (so s 2 = c , s 2 = d , or s 2 = e ) Specifying the payoffs requires that we know the utilities of these two players for each of the eight possible strategy profiles: u 1 ( a, c ) u 2 ( a, c ) u 1 ( a, d ) u 2 ( a, d ) u 1 ( a, e ) u 2 ( a, e ) u 1 ( b, c ) u 2 ( b, c ) u 1 ( b, d ) u 2 ( b, d ) u 1 ( b, e ) u 2 ( b, e ) Todd Sarver (Northwestern University) Game Theory Econ 310-2 – Fall 2011 4 / 30
Depicting a 2-Player Game Using a Matrix Create a matrix (or table) with a row for each strategy for player 1 and a column for each strategy for player 2. Indicate the payoffs to each player for each strategy profile in the appropriate cell in the matrix. Todd Sarver (Northwestern University) Game Theory Econ 310-2 – Fall 2011 5 / 30

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

View Full Document
Depicting a 2-Player Game Using a Matrix Create a matrix (or table) with a row for each strategy for player 1 and a column for each strategy for player 2. Indicate the payoffs to each player for each strategy profile in the appropriate cell in the matrix.
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