发表机构
University of Trento; University of Milano-Bicocca（特伦托大学; 米兰比可卡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对加密货币合并缺乏公平汇率框架的问题，本文提出内生合并价值的形式化框架，证明价格比率在特定条件下满足五项公平条件，并揭示流动性是唯一可能破坏容许集的非财富因素。
AI 中文摘要
在现存的数千种加密货币中，许多都面临采用率下降、流动性不足和安全性薄弱的问题，将其中两种合并为一个单一生态系统是替代放弃策略的自然选择。然而，目前尚无严谨的框架来确定此类合并中的公平汇率。与公司不同，加密货币的价值由网络效应驱动，因此汇率本身会影响合并后资产的价值。我们扩展了Mainini、Moretto和Visetti [7]的汇率比率框架，使合并价值内生化：汇率决定社区迁移，迁移（在考虑用户重叠的情况下）决定合并后的网络状态，而一个公理化的估值函数为该状态赋予价值。由此产生的协同效应没有预定符号，谈判区域的边界在汇率上变得自指。我们证明了不存在一个使合并破坏价值的汇率能够保全财富，并且合并前价格比率在且仅在该汇率下合并不破坏价值时能够精确保全财富。在这种情况下，在明确的阈值条件下，价格比率满足我们全部五个公平条件——财富保全、采用率、安全性、治理和流动性保全——并且在这些条件的严格版本下，容许集包含围绕该比率的一个非退化区间，财富容许集具有明确宽度。文献中提出的网络价值定律，从线性定律到Metcalfe定律及其广义幂律形式，共享一个凸性性质，该性质产生了支撑这些估计的Lipschitz控制。流动性成为唯一可能断开容许集的非财富条件。
英文摘要
Many of the thousands of existing cryptocurrencies suffer from declining adoption, low liquidity and weak security, and merging two of them into a single ecosystem is a natural alternative to abandonment. No rigorous framework exists, however, for determining a fair exchange rate in such a merger. Unlike that of a corporation, the value of a cryptocurrency is driven by network effects, so the exchange rate itself influences the value of the merged asset. We extend the exchange-ratio framework of Mainini, Moretto and Visetti [7] by making the merged value endogenous: the exchange rate determines community migration, migration determines (up to user overlap) the post-merger network state, and an axiomatised valuation function assigns a value to that state. The resulting synergy has no predetermined sign, and the bounds of the bargaining region become self-referential in the exchange rate. We prove that no exchange rate at which the merger destroys value preserves wealth, and that the pre-merger price ratio preserves wealth exactly when the merger does not destroy value at that rate. In that case, under explicit threshold conditions, the price ratio satisfies all five of our fairness conditions -- wealth, adoption, security, governance and liquidity preservation -- and, under strict versions of these conditions, the admissible set contains a nondegenerate interval around it, the wealth-admissible set one of explicit width. The network-value laws proposed in the literature, from the linear law to Metcalfe's and its generalised power-law forms, share a convexity property that yields the Lipschitz control behind these estimates. Liquidity emerges as the only non-wealth condition that can disconnect the admissible set.
