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Is Emulation Good for You? The Ups and Downs of Rivalry

We model the emulation between two athletes whose goals are fixed by their coaches. The coaches in turn engage in a game of goal setting. We analyze the equilibriums of that game. For some range of parameter values, there are only mixed equilibriums, where one coach randomizes his goals while the other coach uses a pure strategy. We show that it is in an athlete's interest to have a stronger rival. Both athletes can gain if there is not a big gap between their ability levels. A very big gap, however, result in poorer performance of both.
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