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This is presumably constructed by taking:
:<math>\Pi = \int_0^{\infty} \left \underbrace{pr(\tau(x_i) \le \min(\hat{\tau_i},t)}_{\mbox{Prob of winning at t}} \cdot \underbrace{PV_t (V)}_{\mbox{PV of V at t}} \right ) dt - \underbrace{x}_{\mbox{cost}}\;</math>
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