What levels of total abatement can one hope for in a global climate agreement? Some potential answers to this question are provided by game theory. This working paper contains a critical discussion of two (prominent) game models that answer the question quite pessimistically. Both models take the n-person, infinitely repeated prisoner's dilemma game as their point of departure. The first model is a full information model and utilizes the notion of a weakly renegotiation proof equilibrium. This results in the (maybe counterintuitive) prediction that an agreement that can provide high utility to the group will attract less total abatement than an agreement that can only provide low utility to the group. The second model assumes imperfect public information and utilizes the notion of a trigger level equilibrium. This results in the (more intuitive) prediction that the level of total abatements will increase with improved verification techniques, for a given player set. Still the level of total abatements decrease with an increasing player set, for a given verification technique. Empirical implications of the two models are identified, and it is argued that one should confront these with experimentally generated data in order to discriminate between the models. One reason for this is that historical data on abatement efforts in a global climate agreement do not exist since no such agreement has entered into force yet.