{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture7

# lecture7 - Lecture 7 Game Theory Key Terms in Lecture Mixed...

This preview shows pages 1–8. Sign up to view the full content.

Lecture 7: Game Theory

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

View Full Document
Key Terms in Lecture Mixed strategies Continuum of actions Tragedy of the commons
Mixed Strategies When a player chooses one action or another with certainty, he is following a pure strategy Players may also follow mixed strategies randomly select from several possible actions DO NOT MISINTERPRET THE WORD “random” You may have a plan to turn left half the time and right half the time. These probabilities need not have been “randomly” selected. But given these probabilities, your action cannot be predicted perfectly. This is what we mean by “random”

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

View Full Document
Mixed Strategies Reasons for studying mixed strategies – some games have no Nash equilibrium in pure strategies but will have one in mixed strategies (i.e. Rock, paper, scissors) – strategies involving randomization are familiar and natural in certain settings Rock, paper, scissors A pitcher’s pitch selection (usually) • Others?
Mixed Strategies Suppose that player i has a set of M possible actions, A i = { a 1 i , …a m i ,…, a M i } A mixed strategy assigns a probability top each of the M actions Obviously, these probabilities must add to 1 Obviously, each probability must be between 0 and 1 Example: A player can either turn Right or Left. Let r be the probability she turns right and l be the probability she turns left. Then r + l = 1 and 0 ! r ! 1 (equivalently 0 ! l ! 1)

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

View Full Document
Mixed Strategies A pure strategy is a special case of a mixed strategy – only one action is played with positive probability – In the previous example, either r = 1 or l = 1 Mixed strategies that involve two or more actions being played with positive probability are called strictly mixed strategies – In the previous example, 0 < r < 1
Expected Payoffs

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 ]}

### Page1 / 22

lecture7 - Lecture 7 Game Theory Key Terms in Lecture Mixed...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online