ps8fall2000 - 14.03 Fall 2000 Problem Set 8 (OPTIONAL, NOT...

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1 14.03 Fall 2000 Problem Set 8 (OPTIONAL, NOT FOR CREDIT): Game Theory and Network Externalities Theory: 1. Consider the following game: Player 2 ABCD Player 1 Up 1, 1 2, 2 3, 4 9, 3 Down 2, 5 3, 3 1, 2 7, 1 a) Find all the pure-strategy Nash Equilibria. b) Find a mixed-strategy Nash Equilibrium of the game. 2. Consider the following game. Firm E (entrant) is considering entering a market that currently has a single incumbent (firm I). If it does so (playing “in”), the incumbent can respond in one of two ways: it can either accommodate the entrant, giving up some of its sales but causing no change in the market price, or it can fight the entrant, engaging in a costly market war that dramatically lowers the market price. The extensive form of this game is depicted below a) Represent the game in Normal Form and find all the pure strategy Nash Equilibria. Firm E Firm I In Out Accommodate Fight ö ç ç è æ = = 2 0 I E U U ö ç ç è æ = = 1 3 I E U U ÷ ÷ ö ç ç è æ = = 1 2 I E U U
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2 b) Using the extensive form, find the Subgame Perfect Nash Equilibria. Compare your result to the one found in part (a) and discuss. 3. Firm 1 and Firm 2 are competing for a cable television franchise. The present value of the net revenues generated by the franchise is equal to R. Each firm’s probability of winning the franchise is given by its proportion of the total spent by the two firms on lobbying the local government. That is, if 1 L and 2 L represent the lobbying expenditures of firms 1 and 2, respectively, then Firm 1’s probability of winning is given by ) /( 2 1 1 L L L + , and Firm 2’s probability of winning is ) /( 2 1 2 L L L + . A. If each firm assumes that the other firm’s spending is independent of its own, what is the Nash equilibrium level of spending for each firm? 2 * 1 * , L L B. The head of Firm 1 meets the head of Firm 2 at the golf club and says, “It’s silly for us to spend 2 * 1 * , L L on lobbying when in the end, we each only have a 50 percent chance of getting the franchise. Why don’t we each spend zero and the outcome will (on average) be the same but we’ll both be better off by 2 * 1 * , L L .” The head of Firm 1 says, “You know, that makes a lot of sense.” How much does each spend on lobbying in the next period, and why? 4. The countries of North and South are in a dispute over fishing rights in George’s Bank, a fertile fishing ground off the coast of New England. The source of disagreement is that each boat sent into George’s Bank reduces the yield of all of the other boats.
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This note was uploaded on 03/18/2012 for the course ECON 201 taught by Professor Çakmak during the Spring '10 term at Middle East Technical University.

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ps8fall2000 - 14.03 Fall 2000 Problem Set 8 (OPTIONAL, NOT...

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