IS EMULATION GOOD FOR YOU? THE UPs AND DOWNs OF RIVALRY

We introduce the notion of emulation that accounts for the effect of another participant's goals on the probability of success of an individual in the context of a sporting contest. The individual not only chooses her effort to maximize utility, but also reacts to the goals set by her own coach and the coach of another individual. We analyse the game of goal setting between two coaches. Beginning with identically able athletes, as one athlete's ability increases, both athletes' set goals are increased but the more able one's increases faster at first. At some critical point the coach of the less able athlete shifts to a mixed strategy that pins the other coach to a single pure strategy.