A question in the design of carbon dioxide trading systems is how allowances are to be initially allocated: by auction, by giving away fixed amounts, or by allocating based on output, fuel, or other decisions. The latter system can bias investment, operations, and pricing decisions, and increase costs relative to other systems. A nonlinear complementarity model is used to investigate long-run equilibria that would result under alternative systems for power markets characterized by time varying demand and multiple generation technologies. Existence of equilibria is shown under mild conditions. Solutions show that allocating allowances to new capacity based on fuel use or generator type can distort generation mixes, invert the operating order of power plants, and inflate consumer costs. The distortions can be smaller for tighter CO2 restrictions, and are somewhat mitigated if there are also electricity capacity markets or minimum-run restrictions on coal plants.