There exist an oligopoly(duopoly) of two firms, both of which are identical in terms of their production costs. If the two firms can cooperate, what should they do to maximise industry profits?

How does your answer change if the two firms have different costs of production?

If you are a consultant from the government, how would you view the proposed cooperation between these two firms?

Assuming that both firms can communicate (via the business press) on their plans, prices and agendas (though it might not be credible). Using an economic model, how might it be difficult to sustain a cooperative (high profit) outcome?

If firms are not allowed to explicitly coordinate their prices. Are there other ways in which two large firms can try to avoid being caught in a competitive outcome?