1 Transaction Fee Mechanism for Finite Block Size (30 points) Recall that Bitcoin runs a first price auction, i.e., highest bids are confirmed and each confirmed transaction pays its own bid. In this problem, we will consider a tweak, that is, a first price auction with a reserve price. Roughly speaking, there is a fixed reserve price r that serves as a cutoff, and any bid that is lower than r will be ignored. We then run a first price auction over the remaining bids. More formally, consider the following transaction fee mechanism. Let k be the block size, and let r be a fixed reserve price. - Inclusion rule: Let the candidate set S={b1,,bN} be the set of bids that bid at least r, where b1bN. If Nk, then include all of S in the block. Else, include (b1,,bk) in the block; that is, include the top k bids from S. - Confirmation rule: All bids included in the block are confirmed (we assume that only bids that are at least r can be included; any bid that is less than r will be ignored even if included). - Payment rule: For each confirmed bid b, it pays b; that is, it pays its own bid. - Miner revenue rule: The miner gets all the payment. You are asked to analyze this suggested transaction fee mechanism. 1. Is this mechanism UIC? If your answer is yes, you do NOT need to write a proof. If your answer is no, please describe a strategy that allows a user to benefit. 2. Is this mechanism MIC? If your answer is yes, you do NOT need to write a proof. If your answer is no, please describe a strategy that allows the miner to benefit. 3. Is this mechanism 1-SCP? If your answer is yes, you do NOT need to write a proof. If your answer is no, please describe a strategy that allows a miner-user coalition (with only one user) to benefit. 1 Transaction Fee Mechanism for Finite Block Size (30 points) Recall that Bitcoin runs a first price auction, i.e., highest bids are confirmed and each confirmed transaction pays its own bid. In this problem, we will consider a tweak, that is, a first price auction with a reserve price. Roughly speaking, there is a fixed reserve price r that serves as a cutoff, and any bid that is lower than r will be ignored. We then run a first price auction over the remaining bids. More formally, consider the following transaction fee mechanism. Let k be the block size, and let r be a fixed reserve price. - Inclusion rule: Let the candidate set S={b1,,bN} be the set of bids that bid at least r, where b1bN. If Nk, then include all of S in the block. Else, include (b1,,bk) in the block; that is, include the top k bids from S. - Confirmation rule: All bids included in the block are confirmed (we assume that only bids that are at least r can be included; any bid that is less than r will be ignored even if included). - Payment rule: For each confirmed bid b, it pays b; that is, it pays its own bid. - Miner revenue rule: The miner gets all the payment. You are asked to analyze this suggested transaction fee mechanism. 1. Is this mechanism UIC? If your answer is yes, you do NOT need to write a proof. If your answer is no, please describe a strategy that allows a user to benefit. 2. Is this mechanism MIC? If your answer is yes, you do NOT need to write a proof. If your answer is no, please describe a strategy that allows the miner to benefit. 3. Is this mechanism 1-SCP? If your answer is yes, you do NOT need to write a proof. If your answer is no, please describe a strategy that allows a miner-user coalition (with only one user) to benefit