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Solution to exchanges 10.3 puzzle: contingency exigency

Solution to exchanges 10.3 puzzle: contingency exigency Solution to Exchanges 10.3 Puzzle: Contingency Exigency ROBIN J. RYDER CEREMADE, Universit´ Paris-Dauphine e First, a quick recap of the problem: the payout is a random variable X; we assume we know its distribution F , and in particular that we know EF [X]. We are looking for a function (·, ·) such that EF [(t, X)] = r · t, where r is the non-contingency hourly rate. Initially, we impose that t, (t, 0) = 0 and that is linear in t. 1. First, consider the problem with no minimum payment. The second condition implies that we can write (t, X) = t·g(X) for some function g. There are infinitely many functions g which would work. The simplest one is to take g(X) = · X. The formula (t, X) = · X · t means that the agent's hourly rate is a percentage of the total winnings (as opposed to the more classical scheme where the total payment is a percentage of the winnings, independently of time spent). All we have to do is find . This is easy enough: EF [(t, X)] = r · t EF [ · t · X] = r · http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGecom Exchanges Association for Computing Machinery

Solution to exchanges 10.3 puzzle: contingency exigency

Ryder, Robin J.
ACM SIGecom Exchanges , Volume 11 (2) – Dec 1, 2012
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Publisher
Association for Computing Machinery
Copyright
Copyright © 2012 by ACM Inc.
ISSN
1551-9031
DOI
10.1145/2509002.2509012
Publisher site
See Article on Publisher Site

Abstract

Solution to Exchanges 10.3 Puzzle: Contingency Exigency ROBIN J. RYDER CEREMADE, Universit´ Paris-Dauphine e First, a quick recap of the problem: the payout is a random variable X; we assume we know its distribution F , and in particular that we know EF [X]. We are looking for a function (·, ·) such that EF [(t, X)] = r · t, where r is the non-contingency hourly rate. Initially, we impose that t, (t, 0) = 0 and that is linear in t. 1. First, consider the problem with no minimum payment. The second condition implies that we can write (t, X) = t·g(X) for some function g. There are infinitely many functions g which would work. The simplest one is to take g(X) = · X. The formula (t, X) = · X · t means that the agent's hourly rate is a percentage of the total winnings (as opposed to the more classical scheme where the total payment is a percentage of the winnings, independently of time spent). All we have to do is find . This is easy enough: EF [(t, X)] = r · t EF [ · t · X] = r ·

Journal

ACM SIGecom Exchanges – Association for Computing Machinery

Published: Dec 1, 2012

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