||Delegated quantum computing enables a client with a weak computational power to delegate quantum computing to a remote quantum server in such a way that the integrity of the server is efficiently veried by the client. Recently, a new model of delegated quantum computing has been proposed, namely, rational delegated quantum computing. In this model, after the client interacts with the server, the client pays a reward to the server depending on the server's messages and the client's random bits. The rational server sends messages that maximize the expected value of the reward. In this talk, we propose novel one-round rational delegated quantum computing protocols by generalizing the classical rational sumcheck protocol. We also discuss the reward gap. Simply speaking, the reward gap is a minimum loss on the server's reward incurred by a server's behavior that makes the client accept an incorrect answer. Apart from these results, we show, under a certain condition, the equivalence between rational and ordinary delegated quantum computing protocols.