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Unformatted text preview: Econ 171 Spring 2010 The Extensive Form and Subgame-Perfect Nash Equilibrium April 22 Preliminaries • Outline 1. In-class games, payment 2. Extensive form basics 3. Extensive vs. Normal form 4. Backwards Induction 5. SPNE 6. Application: Stackelberg Duopoly Two In-Class Games Sequential BoS: Role determined by coin flip, even vs. odd perm number being Player 1. Player 2: contingent plan: choice if 1 chooses O, if 1 chooses B. Results, payment. Then, select two cards at random for grab game. Start with 1 dollar in hand. Player 1 grabs or passes. Add 1 dollar then player 2 grabs or passes. When pot hits $7, passing give both players $0. Extensive form basics • Node: where a decision occurs; Branches, represent individual actions. Write down example. Initial, vs. decision vs. terminal node vs. chance. Player actions and labels: don’t use same labels in different places. • Information sets. Players know structure of tree, but not necessarily where they are in the tree. Info set is a place where decision is made. • outcomes represented by terminal nodes, payoffs represent preferences, just like in normal form. Three examples: Sequential BoS, BoS: perfect vs. imperfect information Centipede List strategies in each case. Tree rules: • Every node is the successor of the initial node, and the initial node is the only one with this property. 1 • Every node except initial node has exactly 1 immediate predecessor. Initial node has none. • Multiple branches extending from the same node have different action labels • Each information set contains decision nodes for only one player. • All nodes in a given information set must have the same number of immediate succes- sors and they must have the same set of action labels on the branches leading to these successors....
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- Fall '08
- Game Theory, Nash, Normal Form, sequential bos