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In Tim Roughgarden's fantastic course on Algorithmic Game Theory, he begins the course by introducing basic mechanism design, and Myerson's Lemma. 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.

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  • $\begingroup$ 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. $\endgroup$ – Michael Greinecker Aug 30 '18 at 20:25
  • $\begingroup$ Equation (7) of your linked PDF (and the text immediately preceding) answer your question in the affirmative. $\endgroup$ – kyle Nov 30 '18 at 4:56
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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.

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  • $\begingroup$ 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. $\endgroup$ – Kitsune Cavalry Dec 29 '18 at 17:49

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