We propose a novel hypergraph information structure for a Cournot network competition model and formulate it as a distributed optimization problem which we solve with continuous-time evolutionary game theoretic techniques that result in a dynamical system. The proposed hypergraph structure is more efficient and compact in terms of information transmission than a bipartite graph and exhibits faster convergence of the respective distributed evolutionary dynamical system. The equilibrium point of the distributed evolutionary dynamical system is unique and has the economic interpretation of the market clearing point. Thus, fast attainment is associated with economic benefits like price stability and efficient resource allocation.