The cloud service broker (CSB) has to ensure intermediation for cloud services. Especially, it acts as an interface among customers and providers of cloud resources. The main purpose of the CSB is to pertinently aggregate different demands of customers into a global demand. The objective is to obtain a price for this global demand as low as possible from the providers. Finding the best aggregations of demands is an optimisation problem. In a competitive context between providers, this optimisation problem has to be solved taking into account partial knowledge. We model this problem as a game in which we evaluate the quality of Nash equilibria from the optimisation problem point of view. We propose to use a linear reward inaction algorithm to reach such equilibria in a partial knowledge and distributed context after proving a convergence property of the algorithm. This approach is finally experimented by numerous simulations.