In the face of limited block size, miners (e.g., in Bitcoin) typically prioritize transactions with the highest bids, which increasingly make up a larger portion of their revenue. If the block size were to expand significantly, meeting all transaction demand due to infrastructure or protocol improvements, bids could drop to zero or to a constant minimum fee. This would diminish miners’ incentives to mine, potentially affecting network security. To address this, Lavi et al. [15] study a monopolistic pricing mechanism where miners may not fill the entire block but only include transactions that pay a minimum price set by the miner. This mechanism aims to be incentive-compatible and allows miners to collect some revenue, although it may result in an unbounded loss in welfare. Nisan [19] expands this by modeling bidders as patient, meaning they are willing to wait without cost until block prices drop low enough for their transactions to be included, leading to wildly fluctuating prices even when demand is stable and there is no stochastic element in the model. In order to capture users’ diminishing interest in having their transactions added to the ledger over time, we consider a more realistic setting with quasi-patient users, where only a fraction \(\delta \in [0,1]\) of pending transactions remains in the next round. This richer model encompasses both Lavi et al.’s [15] impatient users ( \(\delta =0\) ) and Nisan’s [19] patient users ( \(\delta =1\) ) as special cases. We demonstrate that Nisan’s fluctuating dynamics persist for \(\delta \) close to 1, while for \(\delta \) close to 0, the dynamics resemble the impatient case. For \(\delta \in (0,1)\) , we establish new bounds on price dynamics, revealing unexpected effects. Unlike the fully patient case, the bounds of the dynamics for \(\delta <1\) depend on the demand curve and undergo a “transition phase”. For some \(\delta \) , the model mirrors the fully patient setting, and for smaller \(\delta ' < \delta \) , it stabilizes at the highest monopolist price, thus collapsing to the impatient case. We provide quantitative bounds and analytical results, showing that the bounds for \(\delta =1\) are generally not tight for \(\delta <1\) , and we give guarantees on the minimum (“admission”) price for transactions.

Serial Monopoly on Blockchains with Quasi-patient Users

会议论文
发表日期：

2026年

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Paolo Penna,
Manvir Schneider

摘要

In the face of limited block size, miners (e.g., in Bitcoin) typically prioritize transactions with the highest bids, which increasingly make up a larger portion of their revenue. If the block size were to expand significantly, meeting all transaction demand due to infrastructure or protocol improvements, bids could drop to zero or to a constant minimum fee. This would diminish miners’ incentives to mine, potentially affecting network security. To address this, Lavi et al. [15] study a monopolistic pricing mechanism where miners may not fill the entire block but only include transactions that pay a minimum price set by the miner. This mechanism aims to be incentive-compatible and allows miners to collect some revenue, although it may result in an unbounded loss in welfare. Nisan [19] expands this by modeling bidders as patient, meaning they are willing to wait without cost until block prices drop low enough for their transactions to be included, leading to wildly fluctuating prices even when demand is stable and there is no stochastic element in the model. In order to capture users’ diminishing interest in having their transactions added to the ledger over time, we consider a more realistic setting with quasi-patient users, where only a fraction \(\delta \in [0,1]\) of pending transactions remains in the next round. This richer model encompasses both Lavi et al.’s [15] impatient users ( \(\delta =0\) ) and Nisan’s [19] patient users ( \(\delta =1\) ) as special cases. We demonstrate that Nisan’s fluctuating dynamics persist for \(\delta \) close to 1, while for \(\delta \) close to 0, the dynamics resemble the impatient case. For \(\delta \in (0,1)\) , we establish new bounds on price dynamics, revealing unexpected effects. Unlike the fully patient case, the bounds of the dynamics for \(\delta <1\) depend on the demand curve and undergo a “transition phase”. For some \(\delta \) , the model mirrors the fully patient setting, and for smaller \(\delta ' < \delta \) , it stabilizes at the highest monopolist price, thus collapsing to the impatient case. We provide quantitative bounds and analytical results, showing that the bounds for \(\delta =1\) are generally not tight for \(\delta <1\) , and we give guarantees on the minimum (“admission”) price for transactions.