cartels

[gusl]

If a drought destroys units of a certain crop, whose demand is inelastic, uniformly across producers, then all the producers benefit. This is slightly paradoxical, but it's true: cartels form precisely to artificially create such a situation of scarcity: if producing 1% less makes the prices 10% higher, then it makes sense to limit production.

But a natural disaster is still the best way of coordinating, preventing cheating from cartel members, and not discouraging producers from working hard.

Do game theorists have a simple, standard formal game for modeling cartels?