Greenhouse gas emission trading has become more and more important in the context of climate change. Recently, a discussion on trading on entity (i.e. company) level has started. Emitters likely to be obliged to participate have argued for an initial allocation of the emission rights free of charge. I analyse the implication of such an allocation based on historical emissions and on benchmarks in multi-period emission trading. Different allocation rules for successive periods are applied, namely allocations with reference figures that are either constant or that change over time. The analysis is carried out using a two-player, two-period model. I find that – depending on their marginal abatement cost - participants have different preferences with regard to the allocation method over time as individual compliance cost can change, too. Total costs remain, however, unaffected by the individual allocations as emissions are reduced where abatement is cheapest. Furthermore, I show that, depending on the allocation method, incentives exist to increase emissions in one period in order to get more emission rights in a subsequent period.