Optimal coalition splitting with heterogenous strategies

We consider a group of players initially members of a coalition managing cooperatively a
public bad, in this case, the stock of pollution. Countries are technologically heterogeneous
but the pollution damage is uniform. We essentially attempt to characterize the conditions
under which a country may eventually split and when it splits within an infinite horizon
multi-stage differential game. In contrast to the existing literature, we do not assume
that after splitting, the splitting player and the remaining coalition will adopt Markovian
strategies. Instead, we assume that the latter will remain committed to the collective control
of pollution and play open-loop, while the splitting player plays Markovian. Within a full
linear-quadratic model, we characterize the optimal strategies. We later compare with the
outcomes of the case where the splitting player and the remaining coalition play both
Markovian. We highlight several interesting results in terms of the implications for long-
term pollution levels and the duration of coalitions with heterogeneous strategies.