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"Consider an auction, with reserve price $X$ chosen from distribution $G$ where the item is allocated to a uniformly chosen random bidder among those who bid above the reserve price. The winner pays $X$, the reserve. Show that this auction is truthful, that is that the optimal strategy is to bid your value."

I just need a little direction to get started, I'm wondering how to show that bidding value $V$ is indeed the optimal strategy in an auction like this.

Brian Fitzpatrick
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Alex
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1 Answers1

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Given the structure of the auction, the only thing about your bid which affects your payoffs is whether your bid is above the reserve price or not. Now consider separately the cases of a player whose valuation is higher than the reserve price and that of a player whose valuation is lower than the reserve price.

Jyotirmoy Bhattacharya
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