Paper: arXiv 2609.39264

Authors: Massimiliano Sala, Daniela Visetti

Abstract

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a highly novel and mathematically sophisticated framework for cryptocurrency mergers, extending existing corporate finance models. While strong in theory and formal proofs, it lacks empirical validation or backtesting, which is acknowledged as future work. The clarity is good for a theoretical paper, but the lack of empirical application limits its immediate practical rigor.

Research Flowchart

  flowchart TD
    A[Research Goal: Fair Exchange Rate for Crypto Mergers?] --> B{Methodology: Extended Mainini et al. Framework};
    B --> C[Inputs: Cryptocurrencies, Network States, Valuation Axioms, User Overlap];
    C --> D{Computational Process: Endogenous Merged Value & Network Effects};
    D --> E[Key Findings: Wealth Preservation, Fairness Conditions, Admissible Set];