Calculate the best dynamic threshold-strategies

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Reference no: EM133930576

Assignment:

You play the following game: At each time t = 1,...,n, you see a prize of value of xt, and you need to decide whether to take it and go home, or continue to the rest of the prizes. All xt are distributed independently from the uniform distribution over [0, 1]. A dynamic threshold-strategy is described by τ1 , . . . , τn , where you select the first xi that exceeds the corresponding τi. A static threshold-strategy is described by a single parameter τ where you select the first xi that exceeds τ.

a. Calculate the best dynamic threshold-strategies for n = 2, 3, along with their expected performances.

b. Calculate the best static threshold-strategies for n = 1, 2, along with their expected performances.

c. What is the expectation of the best dynamic threshold as a function of n (write a recursive formula)?

Reference no: EM133930576

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