First, the equilibrium properties are compared for general Cournot and Stackelberg two-person games with symmetric payoff functions. Second, labor-managed Cournot and Stackelberg duopoly equilibria are compared. Under our assumptions, the Cournot firm's output is larger than the Stackelberg follower's output, which in turn is larger than the leader's output. Dividend per unit of labor is larger for the Stackelberg follower than for the Stackelberg leader, which in turn gets larger dividend per unit of labor than the Cournot firm.