This paper introduces the Repeated Rational Secret Sharing problem. We borrow the notion of rational secret sharing from Halpern and Teague, where players prefer to get the secret than not to get the secret and with lower preference, prefer that as few of the other players get the secret. We introduce the concept of repeated games in the rational secret sharing problem for the first time, which enables the possibility of a deterministic protocol for solving this problem. This is the first approach in this direction to the best of our knowledge. We extend the results for the mixed model (synchronous) where at most t players can be malicious. We also propose the first asynchronous protocol for rational secret sharing. © 2008 Springer-Verlag Berlin Heidelberg.