This paper introduces the concept of rationality-based computing (RBC) and a preliminary design of middleware, GameMosix, that implements the concept. Millions of computers and mobile devices over the Internet play rationality-based games in sharing computational resources. Researchers in computer systems communities are becoming more interested in game theory and evolutionary computing. First, we discuss previous work on game theory and evolutionary game theory applied to computer systems. Then we introduce the design of a preliminary version of RBC middleware architecture and some results from the simulation of the architecture.