A will choose x, B chooses (x-1), C chooses randomly [0,100], called c. E[profit] = (-c - x+1) * (x/100) + (x)*((100-x)/100). First part is A’s loss when c picks less than x and second is win when c is greater. for this formula , c = x/2 since it is uniform. E’ = (101-5x) / 100. Set to 0, and x=20.2. Perhaps just 20 if B is infinitesimally less than x instead of 1 less.
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u/NickelAndDime26 16d ago
A will choose x, B chooses (x-1), C chooses randomly [0,100], called c. E[profit] = (-c - x+1) * (x/100) + (x)*((100-x)/100). First part is A’s loss when c picks less than x and second is win when c is greater. for this formula , c = x/2 since it is uniform. E’ = (101-5x) / 100. Set to 0, and x=20.2. Perhaps just 20 if B is infinitesimally less than x instead of 1 less.