This paper describes simulations in an artificial society in which autonomous agents exchange gifts. In this society agents perform simple acts that are looked at by the others and are analysed so that a common image is created for each agent (a reputation). The model is based on numerous descriptions of non-merchant exchange systems, which are very interesting for ethnologists as well as for economists: they appear to be important for circulation of goods and to insure the reproduction of social links and values. In the system built the agents must make a gift at each time-step. There exist two kinds of gifts and two corresponding kinds of reputation: the agents either give to share or to be prestigious. Since gifts are received according to status, receiving a gift is as important for a reputation as making one. Each agent is characterised by its "motivation" to acquire the reputation of being a sharing agent or a prestigious agent. It is also characterised by its "esteem", to decide if it will be able to do the gift it wants to do for a time-step. These two characteristics of an agent can be stable during the simulation, but can also evolve according to its history. We study here the different patterns that can appear in the societies, in terms of generation of reputation, and of histories over time. A huge range of these patterns can be observed, depending on the choice made for the parameters. In some cases the agents cannot be individually distinguished, in other cases they can: but, in any case any individual behaviours that emerge have to be sustained by a collective specification that points out more or less the way agents value each reputation.