lecture10 - Lecture X: Extensive Form Games Markus M....

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Unformatted text preview: Lecture X: Extensive Form Games Markus M. M¨obius March 17, 2004 • Gibbons, chapter 2 • Osborne, sections 5.1, 5.2 and chapter 6 1 Introduction While models presented so far are fairly general in some ways it should be noted that they have one main limitation as far as accuracy of modeling goes- in each game each player moves once and moves simultaneously. This misses common features both of many classic games (bridge, chess) and of many economic models. 1 A few examples are: • auctions (sealed bid versus oral) • executive compensation (contract signed; then executive works) • patent race (firms continually update resources based on where oppo- nent are) • price competition: firms repeatedly charge prices • monetary authority and firms (continually observe and learn actions) Topic today is how to represent and analyze such games. 1 Gibbons is a good reference for economic applications of extensive form games. 1 2 Extensive Form Games The extensive form of a game is a complete description of 1. The set of players. 2. Who moves when and what their choices are. 3. The players’ payoffs as a function of the choices that are made. 4. What players know when they move. 2.1 Example I: Model of Entry Currently firm 1 is an incumbent monopolist. A second firm 2 has the oppor- tunity to enter. After firm 2 makes the decision to enter, firm 1 will have the chance to choose a pricing strategy. It can choose either to fight the entrant or to accommodate it with higher prices. 2 In Out 1 F A 2-1-1 1 1 2.2 Example II: Stackelberg Competition Suppose firm 1 develops a new technology before firm 2 and as a result has the opportunity to build a factory and commit to an output level q 1 before firm 2 starts. Firm 2 then observes firm 1 before picking its output level q 2 . For concreteness suppose q i ∈ { , 1 , 2 } and market demand is p ( Q ) = 3- Q . The marginal cost of production is 0. 2 1 q 1 =0 q 1 =1 q 1 =2 2 1 2 2 1 2 2 1 2 2 2 2 1 1 2-2-2 2.3 Example III: Matching Pennies So far we assumed that players can observe all previous moves. In order to model the standard matching pennies game in extensive form we have to assume that the second player cannot observe the first player’s move....
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This note was uploaded on 05/19/2010 for the course 412 002 taught by Professor Dingli during the Spring '10 term at École Normale Supérieure.

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lecture10 - Lecture X: Extensive Form Games Markus M....

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