In this paper, we propose a simple oligopoly game model to represent the interactions between coalitions of countries in deploying carbon dioxide removal (CDR) strategies in a steady-state net-zero emission climate regime that could take place by the end of the twenty-first century. The emission quotas and CDR activities obtained in the solution of this steady-state model could then be used as a target for end-of-period conditions in a dynamic integrated assessment analysis studying the transition to 2100. More precisely, we analyze a steady-state situation where m coalitions exist and behave as m players in a game of supplying emission rights on an international emission trading system. The quotas supplied by a coalition must correspond to the amount of CO2 captured through CDR activities in the corresponding world region. We use an extension of the computable general equilibrium model GEMINI-E3 to calibrate the payoff functions and compute an equilibrium solution in the noncooperative game.