We consider a variant of Cournot competition, where multiple firms allocate
the same amount of resource across multiple markets. We prove that the game has
a unique pure-strategy Nash equilibrium (NE), which is symmetric and is
characterized by the maximal point of a "potential function". The NE is
globally asymptotically stable under the gradient adjustment process, and is
not socially optimal in general. An application is in transportation, where
drivers allocate time over a street network.