We characterize equilibria of games with two properties: (i) Agents have the opportunity to adjust their strategic variable after their initial choices and before payoffs occur; but (ii) they can only add to their initial amounts. The equilibrium set consists of just the Cournot-Nash outcome, one or both Stackelberg outcomes, or a continuum of points including the Cournot-Nash outcome and one or both Stackelberg outcomes. A simple theorem that uses agents' standard one-period reaction functions and the one-period Cournot-Nash and Stackelberg equilibria delineates the equilibrium set. Applications include contribution, oligopoly, and rent-seeking games. © 2003 Elsevier Inc. All rights reserved.