This paper deals with a class of games defined on a network flow model. The network represents the transformation process of a commodity from its extraction to its final form through the successive stages of the production system. This could represent for example, the flow of energy from extraction to end-use demand, or the flow of any natural resource (like phosphate rock) from the extraction to the selling of the final products on the market.

We assume that the nodes of the network correspond to different players. A definition of market equilibrium is proposed and characterized through a dynamic programming approach. The case where the players are organized in a coalition structure is also considered.

An illustration of this modelling of commodity market equilibria is given for affine demand laws and quadratic transformation costs.