ECO326H5 Study Guide - Quiz Guide: Nash Equilibrium

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Eco 326 (do not circulate to students!: it is easy to argue that no ne exists if no candidate enters. Also, there is no ne if one candidate enters. Because the candidate who does not enter can enter and choose same position as existing candidate. So if ne exists, it must be more than one candidate enter. Otherwise, one candidate could stay out and be better o . Now consider following cases: two candidates tie with di erent positions. By standard hotelling"s model argument, one candidate has incentive to move to median. Not a ne: two candidates tie with same position but not at median. Similarly, one candidate has incentive to move to median. Not a ne: two candidates tie at the median. Then the candidate who stays out has incentive to enter and choose a location arbitrarily close to median. Not a ne: three candidates tie with three di erent position.

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