The assignment and execution of tasks over the Internet is an inexpensive solution in contrast with supercomputers. We consider an Internet-based Master-Worker task computing approach, such as SETI@home. A master process sends tasks, across the Internet, to worker processors. Workers execute, and report back a result. Unfortunately, the disadvantage of this approach is the unreliable nature of the worker processes. Through different studies, workers have been categorized as either malicious (always report an incorrect result), altruistic (always report a correct result), or rational (report whatever result maximizes their benefit). We develop a reputation-based mechanism that guarantees that, eventually, the master will always be receiving the correct task result. We model the behavior of the rational workers through reinforcement learning, and we present three different reputation types to choose, for each computational round, the most reputable from a pool of workers. As workers are not always available, we enhance our reputation scheme to select the most responsive workers. We prove sufficient conditions for eventual correctness under the different reputation types. Our analysis is complemented by simulations exploring various scenarios. Our simulation results expose interesting trade-offs among the different reputation types, workers availability, and cost.