Reputation systems can be modeled purely on the last move. [definitional]
Consider two image scores, 0 for someone who defected last round and 1 for someone who cooperated last round. Thus the image score depends only on the last move of a player as a donor. Consider two types of players: discriminators, who help only players with image score 1, and defectors, who never help.
DEFINE: Introduces the image score model, a simple binary reputation system based only on a donor's most recent action, contrasted with reciprocal strategies and discriminators who help only the reputably cooperative.
Nowak, M. A., & Sigmund, K, Evolution of Indirect Recip…, loc. 109