With the increasing adoption of blockchain technology, there is a strong need for achieving interoperability between unconnected ledgers. Approaches such as hash time lock contracts (HTLCs) have arisen for cross-chain asset exchange. The solution embraces the likelihood of transaction failure and attempts to "make the best out of worst" by allowing transacting agents to at least keep their original assets in case of an abort. Nonetheless, as an undesired outcome, reoccurring transaction failures prompt a critical and analytical examination of the protocol. In this study, we propose a game-theoretic framework to study the strategic behaviors of agents taking part in cross-chain atomic swaps implemented with HTLCs. We study the success rate of the transaction as a function of the swap rate, the token price and its volatility, as well as other variables. We demonstrate that both agents might decide not to follow the protocol in an attempt to exploit price variations so as to maximize one's own utility. An extension of our model confirms that collateral deposits can improve the transaction success rate, and motivates further research towards collateralization without a trusted third party.