{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture4a - CMSC 498T Game Theory 4a Extensive-Form Games...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Nau: Game Theory 1 Updated 10/5/11 CMSC 498T, Game Theory 4a. Extensive-Form Games Dana Nau University of Maryland
Image of page 1

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

View Full Document Right Arrow Icon
Nau: Game Theory 2 Updated 10/5/11 The Sharing Game Suppose agents 1 and 2 are two children Someone offers them two cookies, but only if they can agree how to share them Agent 1 chooses one of the following options: Øඏ Agent 1 gets 2 cookies, agent 2 gets 0 cookies Øඏ They each get 1 cookie Øඏ Agent 1 gets 0 cookies, agent 2 gets 2 cookies Agent 2 chooses to accept or reject the split: Øඏ Accept => they each get their cookies(s) Øඏ Otherwise, neither gets any 2-0 1-1 0-2 no yes no yes no yes (0,0) (2,0) (0,0) (1,1) (0,0) (0,2) 2’s move 2’s move 2’s move 1’s move
Image of page 2
Nau: Game Theory 3 Updated 10/5/11 Extensive Form The sharing game is a game in extensive form Øඏ A game representation that makes the temporal structure explicit Øඏ Doesn’t assume agents act simultaneously Extensive form can be converted to normal form Øඏ So previous results carry over Øඏ But there are additional results that depend on the temporal structure In a perfect-information game, the extensive form is a game tree : Øඏ Choice (or nonterminal ) node : place where an agent chooses an action Øඏ Edge : an available action or move Øඏ Terminal node : a final outcome Øඏ At each terminal node h , each agent i has a utility u i ( h ) 2-0 1-1 0-2 no yes no yes no yes (0,0) (2,0) (0,0) (1,1) (0,0) (0,2) 2’s move 2’s move 2’s move 1’s move
Image of page 3

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

View Full Document Right Arrow Icon
Nau: Game Theory 4 Updated 10/5/11 Notation from the Book (Section 4.1) H = {nonterminal nodes} Z = {terminal nodes} If h is a nonterminal node, then Øඏ ρ ( h ) = the player to move at h Øඏ χ ( h ) = {all available actions at h } Øඏ σ ( h,a ) = node produced by action a at node h Øඏ h ’s children or successors = { σ ( h,a ) : a χ ( h )} If h is a node (either terminal or nonterminal), then Øඏ h ’s history = the sequence of actions leading from the root to h Øඏ h’ s descendants = all nodes in the subtree rooted at h The book doesn’t give the nodes names Øඏ The labels tell which agent makes the next move 2-0 1-1 0-2 no yes no yes no yes (0,0) (2,0) (0,0) (1,1) (0,0) (0,2) 2 2 2 1 Different notation than I’m used to, so I might not always remember it
Image of page 4
Nau: Game Theory 5 Updated 10/5/11 Pure Strategies Pure strategy for agent i in a perfect-information game: Øඏ Function telling what action to take at every node where it’s i ’s choice i.e., every node h at which ρ ( h ) = i The book specifies pure strategies as lists of actions Øඏ Which action at which node? Øඏ Either assume a canonical ordering on the nodes, or use different action names at different nodes Sharing game: Agent 1 has 3 pure strategies: S 1 = { 2-0, 1-1, 0-2 } Agent 2 has 8 pure strategies: S 2 = { (yes, yes, yes), (yes, yes, no), (yes, no, yes), (yes, no, no), (no, yes, yes), (no, yes, no), (no, no, yes), (no, no, no) } 2-0 1-1 0-2 no yes no yes no yes (0,0) (2,0) (0,0) (1,1) (0,0) (0,2) 2 2 2 1
Image of page 5

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

View Full Document Right Arrow Icon
Image of page 6
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