Brainteaser help
I am having some trouble with this brainteaser from Crack's book.
Here is the question:
You are bidding for a firm whose unknown true value is uniformly distributed between 0 and 1. Although you do not know the true value S of the firm, you do know that as soon as people learn you made a bid the value will double to 2S. Your bid, however will be accepted only if it is at least as large as the original value of the firm. How do you bid to maximize expected payoff?
Here is my solution:
Payoff = 2S - B * p(0 EV of payoff
However the book solution just says to bid anywhere from 0 to 1 and expect to break even. Is my analysis wrong? What is the right answer?
Just curious, who and what are u applying for? PM me.
Your payoff is wrong.
It should be intergral with respect to S, from zero to 1, (2S - B) * 1_(B>S)
Where 1_(B>S) = 1 if B>S, 0 otherwise
This simplifies to integral from zero to B of (2S -B) dS
Which is trivially zero, independent of B.
You can also draw some simple diagrams for a non-analytic proof.
This is not really a brainteaser, more of a mental exercise.
Sorry to revive this thread but I ran into an extremely similar question for a job interview.
Can somebody explain what this function actually is? Is it the probability B>S?
Agreed. Here's an alternative way:
Assuming that 2S = 0 only if S =S, the only way to make a profit is B
hmmm, what if we change the payoff to 1.5*S or to 3S, do we still break even?
Bid close to or equal to 1.
what if the firm's value is 1, and you bid 1.1? Wouldn't that result in a payoff of 2*1 - 1.1 = 0.9? I'm not sure I understand the question correctly.
It's the indicator function. It takes the value 1 when B>S and is 0 otherwise.
Oh, that makes sense. Thanks!
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