To achieve interoperability between unconnected ledgers, hash time lock contracts (HTLCs) are commonly used for cross-chain asset exchange. The solution tolerates transaction failure, and can "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 exchange rate of the swap, the token price and its volatility, among other variables. We demonstrate that in an attempt to maximize one's own utility as asset price changes, either agent might withdraw from the swap. An extension of our model confirms that collateral deposits can improve the transaction success rate, motivating further research towards collateralization without a trusted third party. A second model variation suggests that a swap is more likely to succeed when agents dynamically adjust the exchange rate in response to price fluctuations.