The allowances in an emission trading system (ETS) are commonly allocated for free to the emission-intensive and trade-exposed sector, e.g., in the form of output-based allocation (OBA). Recently an approach combining OBA with a consumption tax has been proposed to mitigate carbon leakage. This paper evaluates the potential outcome in a game of climate policies, by examining the Nash equilibrium outcome of a non-cooperative policy instrument game between regions that regulate their emissions separately. We construct a computable general equilibrium model and investigate the case when regions can choose to supplement their ETS with OBA and/or with a consumption tax, in the presence of another regulating region. In the context of the EU and China, we show how regional interests combined with a national climate target, may lead to different climate policy combinations.