Bargaining over Risky Assets

We analyze the subgame-perfect equilibria of a game where two agents bargain in order to share the risk in their assets that will pay dividends once at some fixed date. The uncertainty about the size of the dividends is resolved gradually by the payment date and each agent has his own view about how the uncertainty will be resolved. As agents become less uncertain about the dividends, some contracts become unacceptable to some party to such an extent that at the payment date no trade is possible. The set of contracts is assumed to be rich enough to generate all the Pareto-optimal allocations. We show that there exists a unique equilibrium allocation, and it is Pareto-optimal. Immediate agreement is always an equilibrium outcome; under certain conditions, we further show that in equilibrium there cannot be a delay. In this model, the equilibrium shares depend on how the uncertainty is resolved, and an agent can lose when his opponent becomes more risk-averse. Finally, we characterize the conditions under which every Pareto-optimal and individually rational allocation is obtainable via some bargaining procedure as the unique equilibrium outcome.