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The timing is as follows:
#The boss pays the subordinate <math>s \;</math> (which may be negative)#The subordinate searches by choosing <math>a\;</math>, where <math>c(a) = \gamma a^2\;</math>
#The subordinate observes the payoffs <math>(X,Y)\;</math>, if the payoff is <math>X_L\;</math> the project is ignored, otherwise the project may be recommended.
#If the project is recommemded then the boss either implements or rejects the project (perhaps seeing the payoffs).
:<math>a^C = \frac{1}{\gamma}\cdot pX_H\;</math>
:<math>a^* = \frac{1}{\gamma}\cdotpcdot p(X_H + Y_H)\;</math>
:<math>\therefore a^* > a^C \; \forall Y_H >0\;</math>
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