In this paper we address the distributed cross-chain swap problem in the blockchain context where multiple agents exchange assets across multiple blockchain systems (e.g. trading Bitcoins for Litecoins or Ethers). We present a mathematical framework allowing to characterize blockchain swap protocols as the combination of a publishing and a commitment phase, where contracts are respectively published and then committed. We characterize the equilibria of existing cross-chain swap protocols (i.e., blockchain swap protocols exchanging assets among different blockchains). More precisely, we prove that following a swap protocol characterized by concurrent publishing of exchange contracts and snap (immediate) assets transfers is a Nash equilibrium. Furthermore, we prove that for protocols with a sequential publishing and commitment of the assets transfers, following the prescribed protocol is a sub-game perfect equilibrium.