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 $\exists\forall\mathsf{DNF}$.

翻译：加密货币的极端估值和波动性要求投资者频繁分散投资，这需依赖安全的交换协议。跨链交换协议允许不信任的各方安全地交换其资产。然而，当前的模型和协议预设了用户对可接受结果的偏好。本文提出了一种通用的交换模型，允许各方指定其对输入和输出资产子集的偏好。研究表明，现有交换协议在此模型下未必是强纳什均衡。本文刻画了具有安全、活跃且为强纳什均衡性质的交换图类别，并给出了该类别的具体协议。进一步，通过从3SAT归约证明判断交换是否属于该类别是NP难的，并通过从$\exists\forall\mathsf{DNF}$归约证明其为$\Sigma_2^{\mathsf{P}}$-完全问题。