Secret sharing allows one to share a piece of information among n participants in a way that only qualified subsets of participants can recover the secret whereas others cannot. Some of these participants involved may, however, want to forge their shares of the secret(s) in order to cheat other participants. Various cheater identifiable techniques have been devised in order to identify such cheaters in secret sharing schemes. On the other hand, Ramp secret sharing schemes are a practically efficient variant of usual secret sharing schemes with reduced share size and some loss in security. Ramp secret sharing schemes have many applications in secure information storage, information-theoretic private information retrieval and secret image sharing due to producing relatively smaller shares. However, to the best of our knowledge, there does not exist any cheater identifiable ramp secret sharing scheme. In this paper we define the security model for cheater identifiable ramp secret sharing schemes and provide two constructions for cheater identifiable ramp secret sharing schemes. In addition, the second construction is secure against rushing cheaters who are allowed to submit their shares during secret reconstruction after observing other participants’ responses in one round. Also, we do not make any computational assumptions for the cheaters, i.e., cheaters may be equipped with unlimited time and resources, yet, the cheating probability would be bounded above by a very small positive number.