Cross-chain Swaps with Preferences

TL;DR

This paper introduces a generalized cross-chain swap model allowing user preferences on asset subsets, characterizes safe protocols, and proves the computational complexity of protocol verification.

Contribution

It extends existing swap protocols to incorporate user preferences, characterizes conditions for protocol safety and equilibrium, and analyzes the computational hardness of protocol verification.

Findings

Existing protocols are not always strong Nash equilibria.

Characterization of swap graphs with safe, live, equilibrium protocols.

Deciding swap protocol membership is NP-hard and $ ext{Sigma}_2^{ ext{P}}$-complete.

Abstract

Extreme valuation and volatility of cryptocurrencies require investors to diversify often which demands secure exchange protocols. A cross-chain swap protocol allows distrusting parties to securely exchange their assets. However, the current models and protocols assume predefined user preferences for acceptable outcomes. This paper presents a generalized model of swaps that allows each party to specify its preferences on the subsets of its incoming and outgoing assets. It shows that the existing swap protocols are not necessarily a strong Nash equilibrium in this model. It characterizes the class of swap graphs that have protocols that are safe, live and a strong Nash equilibrium, and presents such a protocol for this class. Further, it shows that deciding whether a swap is in this class is NP-hard through a reduction from 3SAT, and further is $\Sigma_2^{\mathsf{P}}$-complete through a reduction from $\exists\forall\mathsf{DNF}$.