The evolution and maintenance of cooperation in populations where public goods are equally accessible to all, but inflict a fitness cost on their sole producers, is a long-standing puzzle of evolutionary biology . A typical example of cooperation is the secretion of siderophores by bacteria. Siderophores are organic chelators produced and released in their environment by bacteria in order to get access to iron. These compounds are believed to diffuse homogeneously, so that secretion by a few bacteria benefits the whole colony, resulting in an unstable situation where non-producers are likely to invade the population. Here we show how this picture is nuanced by the importance of spatial effects, by studying the single-cell dynamics of siderophore pyoverdine usage in wild-type micro-colonies of \it P. aeruginosa grown on agar gels. We show that the dynamics of pyoverdine in a clonal population is driven by its exchange between adjacent cells, rather than with the whole colony. This local exchange impacts the fitness of individuals, as would be expected in a continuous variant of a spatial tit-for-tat strategy. Such a strategy is shown to be sufficient to ensure the maintenance of cooperation within the observed range of parameters.