<p>Milgrom's excellent <em>Putting Auction Theory to Work</em> is a reference for what you're looking for. If I'm not mistaken, Myerson's lemma works for quasi-linear payoffs.</p>

CC BY-SA 4.0
2018-12-29T17:49:51.577Z
This answer could be improved by adding a particular page reference within the source you are citing, and maybe giving a brief outline of the argument for the proof.  +1 for giving a straightforward source anyhow.
Kitsune Cavalry
CC BY-SA 4.0
2018-08-31T02:29:04.487Z
2018-08-31T02:29:04.487Z
Pedro Cavalcante
<p>In Tim Roughgarden's fantastic course on Algorithmic Game Theory, he begins the course by introducing basic mechanism design, and <a href="http://theory.stanford.edu/~tim/f13/l/l3.pdf" rel="nofollow noreferrer">Myerson's Lemma</a>. He then proves that Myerson's Lemma is valid for piecewise constant allocation functions. I would like to know if a proof also exists for piecewise <em>linear</em> allocation functions. </p>

CC BY-SA 4.0
2018-08-30T20:25:20.240Z
I'm not sure what exactly you are looking for. Nothing in the statement of the result mentions piecewise anything and any complete proof of the result will cover more special classes of functions.
Michael Greinecker
CC BY-SA 4.0
2018-11-30T04:56:16.343Z
Equation (7) of your linked PDF (and the text immediately preceding) answer your question in the affirmative.
kyle
<mechanism-design>
Is Myerson's Lemma valid for piecewise linear allocation functions?
Joebevo
# Is Myerson's Lemma valid for piecewise linear allocation functions?

(Asked by: username_0 on 2018-08-30)

In Tim Roughgarden's fantastic course on Algorithmic Game Theory, he begins the course by introducing basic mechanism design, and [Myerson's Lemma](http://theory.stanford.edu/~tim/f13/l/l3.pdf). He then proves that Myerson's Lemma is valid for piecewise constant allocation functions. I would like to know if a proof also exists for piecewise *linear* allocation functions.

**Tags:** mechanism-design

> **Comments:**
> **username_1**: I'm not sure what exactly you are looking for. Nothing in the statement of the result mentions piecewise anything and any complete proof of the result will cover more special classes of functions.  
> **username_2**: Equation (7) of your linked PDF (and the text immediately preceding) answer your question in the affirmative.  

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## 1 answers

### Answer by username_3 on 2018-08-31. Score: 1

Milgrom's excellent *Putting Auction Theory to Work* is a reference for what you're looking for. If I'm not mistaken, Myerson's lemma works for quasi-linear payoffs.

> **Comments:**
> **username_4**: This answer could be improved by adding a particular page reference within the source you are citing, and maybe giving a brief outline of the argument for the proof.  +1 for giving a straightforward source anyhow.  

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