This note deals with spatial (multi-market) and multi-commodity versions of the classical Cournot (1838) oligopoly. Our objective is to find non-cooperative equilibria by decomposition techniques. Specifically, ignoring material balances between supply and production, we iteratively compute modified Cournot outcomes in each constituent, single-point market. Such partial equilibria are repeatedly used as input to identify finally their counterpart in the overall structure. Thus, we compute, in recursion, approximate equilibria, separately in each market, and keep on reconciling these with the coupling constraints. The procedure employed is an instance of Douglas-Ranchford (1954) splitting applied to a sum of two maximal monotone operators, one being a trivial orthogonal projection onto a linear circulation space.
Paru en juin 1992 , 13 pages