The rational secret sharing problem (RSS) considers incentivizing rational parties to share their received information to reconstruct a correctly shared secret. Halpern and Teague (STOC’04) demonstrate that solving the RSS problem deterministically with explicitly bounded runtime is impossible, if parties prefer learning the secret than not learning, and they prefer fewer other parties to learn. To overcome this impossibility result, we propose RSS with competition. We consider a slightly different yet sensible preference profile: Each party prefers to learn the secret early and prefers fewer parties learning before them. This preference profile changes the information-hiding dynamics among parties in prior works: First, those who have learned the secret are indifferent towards or even prefer informing others later; second, the competition to learn the secret earlier among different access groups in the access structure facilitates information sharing inside an access group. As a result, we are able to construct the first deterministic RSS algorithm that terminates in at most two rounds. Additionally, our construction does not employ any cryptographic machinery (being fully game-theoretic and using the underlying secret-sharing scheme as a black-box) nor requires the knowledge of the parties’ exact utility function. Furthermore, we consider general access structures.