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Unformatted text preview: MS&E 246: Game Theory with Engineering Applications Feryal Erhun Winter, 2010 Problem Set # 3 Due: February 4, 2010, 5pm; Outside Terman 305 Reading Assignment: Gibbons, Sections 2.1-2.4; and Mas-Colell, Whinston, Green, Sections 7.C, 7.D, 7.E, 9.A, and 9.B. 1. (PhD students can skip this question) The new widget production process that firm 1 is developing is equally likely to have a high or low costs. Firm 1 will learn whether the production process has high costs or low costs at the beginning of next quarter. Then firm 1 can choose whether to build a new plant or not. Firm 2 will not be able to observe the costs of firm 1s new process, but firm 2 will be able to observe whether firm 1 builds a new plant or not. Firm 2 will subsequently decide whether to enter the widget market against firm 1 or not. Firm 2 will make $2 million (in present discounted value of long-run profits) from entering the widget market if firm 1s process has high costs, but firm 2 will lose $4 million from entering the widget market if firm 1s process has low costs. Lower costs in the new process will increase firm 1s profits by $4 million. Building a new plant would add $2 million more to firm 1s profits if the new process has low costs (because conversion to the new process would be much easier in a new plant), but building a new plant would subtract $4 million from firm 1s profits if the new process has high costs. In any event (whether the new process has high or low costs, whether firm 1 builds a new plant or not), firm 2s entry into the widget market would lower firm 1s profits by $6 million. (Both firms are riskentry into the widget market would lower firm 1s profits by $6 million....
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This note was uploaded on 03/04/2011 for the course MS&E 246 taught by Professor Johari during the Winter '07 term at Stanford.
- Winter '07