Edit to make Xuanji happy
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@ -297,7 +297,7 @@ However, kth price auctions have a different kind of serious flaw: they are not
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A more serious issue is \emph{collusion} between the proposer and some transaction senders. A proposer can potentially collude with low-fee transaction senders (eg. suppose there is a single entity, like an exchange or mining pool, that sends such transactions and can be easily negotiated with) that are sending transactions with some fee $f_{low}$. The proposer can ask them to instead send their transactions with fee $f_{high}$, and refund them $f_{high} - \frac{f_{low}}{2}$. The proposer's revenue is now even higher: the proposer benefits from the increased height of the ``rectangle'' of fee revenue that they would get with the ``dummy transaction'' strategy above, but they would also get a portion of the revenue from transactions that they would otherwise have sacrificed. \footnote{For a more detailed treatment of similar issues, see \cite{li2018} and \cite{rothkopf2007}.}
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A more serious issue is \emph{collusion} between the proposer and some transaction senders. A proposer can potentially collude with low-fee transaction senders (eg. suppose there is a single entity, like an exchange or mining pool, that sends such transactions and can be easily negotiated with) that are sending transactions with some fee $f_{low}$. The proposer can ask them to instead send their transactions with fee $f_{high}$, and refund them $f_{high} - \frac{f_{low}}{2}$. The proposer's revenue is now even higher: the proposer benefits from the increased height of the ``rectangle'' of fee revenue that they would get with the ``dummy transaction'' strategy above, but they would also get a portion of the revenue from transactions that they would otherwise have sacrificed. \footnote{For a more detailed treatment of similar issues, see \cite{li2018} and \cite{rothkopf2007}.}
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Hence, both first-price and second-price auctions are unsatisfactory. However, note that these issues are exclusively properties of auctions, and not properties of a fixed-price sale. If being included in the blockchain simply requires paying some $minFee$, then transaction senders have a simple strategy that they can use to set the fee on their transaction. Let $v$ be a user's private valuation for a transaction getting included in the next block. The user would check if $v > minFee$; if it is, they would bid $minFee + \epsilon$ (to provide a slight incentive for the block producer to include the transaction); if $v < minFee$ they would not send the transaction. This is a very simple strategy that does not require knowledge of others' valuations and is optimal for the transaction sender.
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Hence, both first-price and second-price auctions are unsatisfactory. However, note that these issues are exclusively properties of auctions, and not properties of a fixed-price sale. If being included in the blockchain simply requires paying some $minFee$ (which would be burned, rather than given to the miner, to prevent side-dealing between transaction senders and miners allowing free transactions), then transaction senders have a simple strategy that they can use to set the fee on their transaction. Let $v$ be a user's private valuation for a transaction getting included in the next block. The user would check if $v > minFee$; if it is, they would bid $minFee + \epsilon$ (to provide a slight incentive for the block producer to include the transaction); if $v < minFee$ they would not send the transaction. This is a very simple strategy that does not require knowledge of others' valuations and is optimal for the transaction sender.
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\section{Improving the Second Best}
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\section{Improving the Second Best}
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