| We study cooperative outcomes between economic agents in essentially noncooperative, dynamic environments under uncertainty. In the first essay, uncertainty is introduced so as to impede cooperation. We analyze a model with two risk averse agents who engage in risk sharing over an infinite time horizon in the presence of asymmetric information: one agent's stochastic income realizations are his private information. Both agents can opt out of the risk sharing agreement at any time. We prove existence and uniqueness of efficient and incentive compatible sharing rules. We find inefficient risk sharing across states at all times, and show history dependence of efficient sharing rules: consumption strictly increases over time for an agent who is repeatedly hit with a favorable income shock. Under some restrictions on agents' utility functions, we show that after a better history, an agent's consumption is strictly larger. We also prove the existence of a unique stationary wealth distribution in which neither agent becomes impoverished.; In the second essay, the introduction of uncertainty may engender cooperation. We study a dynamic game very like a finitely repeated prisoners' dilemma. A stochastic variable determines period payoffs to mutual cooperation. The resulting stage game is either a prisoners' dilemma or a related game in which cooperation is better than defection in the limit. The probability pt of switching into the cooperative state is allowed to vary over time. We interpret the sequence {lcub}pt{rcub} as a measure of players' optimism. We provide necessary and sufficient conditions on players' optimism that guarantee cooperation for a fixed fraction of time in a long enough game (significant cooperation), so that average payoffs are strictly greater than in the one-shot prisoners' dilemma. We consider games with ex ante uncertainty in which period payoffs only change due to Bayesian updating, and games in which period payoffs follow a Markov process. Though some cooperation can be sustained in the Bayesian game, it fails our necessary condition for significant cooperation. The Markov game satisfies the sufficient condition for significant cooperation. We conclude that the possibility of change rather than initial uncertainty is required to affect players' payoffs. |
