Presentation on YouTube.

We propose an alternative dynamic theory of coalition breakdown. Motivated by recent coalition splitting events, we assume that: i) the payoff sharing rule within coalitions is not necessarily set according to any optimality and/or stability criterion, and, ii) players initially behave as if the coalition will last for ever. If the sharing rule is non-negotiable or if renegotiation is very costly, compliance to these rules may become unbearable for a given member as time passes because the rule, being too rigid, would make exit preferable. We examine this endogenous exit problem in the case of time-invariant sharing rules. Assuming a Nash non-cooperative game after (potential) splitting where players play Markovian, we characterize the solutions of the endogenous exit problem in a linear-quadratic frame with endogenous splitting time. We find that splitting countries are precisely those which use to benefit the most from the coalition. When initial pollution is high, all shares should be low enough and none of the players should detain a payoff share larger than 1/2. If initial pollution is small, we provide with an explicit interval for the sharing rule values preventing the collapse of the coalition.
(with Raouf Boucekkine, Carmen Camacho, Weihua Ruan)