In the rational cryptographic protocol, the two rational players often fall into the prisoner's dilemma, which is also the case for the rational secret sharing we consider in this paper. First, it is proved that rational secret sharing has a sequential equilibrium in the natural state, so that rational participants will fall into the prisoner's dilemma, resulting in no participants being able to reconstruct the secret correctly. Next, to solve this problem, we propose an incentive-compatible rational secret scheme. Specifically, the game tree with imperfect information is constructed to facilitate our analysis and proof, and the strictly dominated strategies are directly eliminated to simplify the game tree. Further more, we describe the motivation of the verifier. Then, we prove that rational players have no motivation to deviate from honest behavior using sequential equilibrium so that rational players can reconstruct the secret correctly. Finally, we complete the simulation using the smart contract and analyze our entire scheme. In addition, the game of our scheme does not need to be repeated multiple times to reach sequential equilibrium, i.e., the game always follows the rational path.

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