In this paper we highlight how, in awarding public contracts, the reputation of the firms does not receive the same consideration in the legislation of different countries. In our analysis we show which are the potential negative consequences of awarding rules that, as in Italy, neglect this factor; consequently our model justifies the practice of those countries in which some kind of reputational mechanisms are utilized. The main economic literature emphasizes that the efficiency of the awarding procedure depends on the type of contractual rules, especially those regarding firm's remuneration. In this work we show the existence of a reverse link: when the enforcement of contractual terms is imperfect, the rules of the awarding mechanism can help to improve the efficiency of the contractual relationship. In some circumstances, awarding rules based only on the contents of each bid are not able to deal with the problem of opportunistic behaviour during the execution of the contract. Our model points out that the public administration can incentive the fairness of the contractor by considering not only the bids of the competitors, but also their different reputation.