Online reputation systems collect, maintain and disseminate reputations as a summary numerical score of past interactions of an establishment with its users. As reputation systems, including web search engines, gain in popularity and become a common method for people to select sought services, a dynamical system unfolds: Experts' reputation attracts the potential customers. The experts' expertise affects the probability of satisfying the customers. This rate of success in turn influences the experts' reputation. We consider here several models where each expert has innate, constant, but unknown level of expertise and a publicly known, dynamically varying, reputation. The specific model depends on (i) The way that experts' reputation affects customers' preferences, (ii) How experts' reputation is modified as a result of their success/failure in satisfying the customers' requests. We investigate several such models and elucidate some of the key characteristics of reputation in such a market of experts and customers.
