Reputation plays a central role in human societies. Empirical and theoretical work indicates that a good reputation is valuable in that it increases one's expected payoff in the future. Here, we explore a game that couples a repeated Prisoner's Dilemma (PD), in which participants can earn and can benefit from a good reputation, with a market in which reputation can be bought and sold. This game allows us to investigate how the trading of reputation affects cooperation in the PD, and how participants assess the value of having a good reputation. We find that depending on how the game is set up, trading can have a positive or a negative effect on the overall frequency of cooperation. Moreover, we show that the more valuable a good reputation is in the PD, the higher the price at which it is traded in the market. Our findings have important implications for the use of reputation systems in practice.