We propose a class of multiple-prior representations of preferences under ambiguity, where the belief the decision-maker (DM) uses to evaluate an uncertain prospect is the outcome of a game played by two conflicting forces, Pessimism and Optimism. The model does not restrict the sign of the DM's ambiguity attitude, and we show that it provides a unified framework through which to characterize different degrees of ambiguity aversion, and to represent the coexistence of negative and positive ambiguity attitudes within individuals as documented in experiments. We prove that our baseline representation, dual-self expected utility (DSEU), yields a novel representation of the class of invariant biseparable preferences (Ghirardato, Maccheroni, and Marinacci, 2004), which drops uncertainty aversion from maxmin expected utility (Gilboa and Schmeidler, 1989). Extensions of DSEU allow for more general departures from independence.

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This paper studies an infinite‐horizon repeated moral hazard problem where a single principal employs several agents. We assume that the principal cannot observe the agents' effort choices; however, agents can observe each other and can be contractually required to make observation reports to the principal. Observation reports, if truthful, can serve as a monitoring instrument to discipline the agents. However, reports are cheap talk so that it is also possible for agents to collude, i.e., where they shirk, earn rents, and report otherwise to the principal. The main result of the paper constructs a class of collusion‐proof contracts with two properties. First, equilibrium payoffs to both the principal and the agents approach their first‐best benchmarks as the discount factor tends to unity. These payoff bounds apply to all subgame perfect equilibria in the game induced by the contract. Second, while equilibria themselves depend on the discount factor, the contract that induces these equilibria is independent of the discount factor.