The concept of a non-extreme-outcome-additive capacity (neo-additive capacity) is introduced. Neo-additive capacities model optimistic and pessimistic attitudes towards uncertainty as observed in many experimental studies. Moreover, neo-additive capacities can be applied easily in economic problems, as we demonstrate by examples. This paper provides an axiomatisation of Choquet expected utility with neo-capacities in a framework of purely subjective uncertainty.

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This paper explores risk-sharing and equilibrium in a general equilibrium set-up wherein agents are non-additive expected utility maximizers. We show that when agents have the same convex capacity, the set of Pareto-optima is independent of it and identical to the set of optima of an economy in which agents are expected utility maximizers and have same probability. Hence, optimal allocations are comonotone. This enables us to study the equilibrium set. When agents have different capacities, matters are much more complex (as in the vNM case). We give a general characterization and show how it simplifies when Pareto-optima are comonotone. We use this result to characterize Pareto-optima when agents have capacities that are the convex transform of some probability distribution. comonotonicity of Paretooptima is also shown to be true in the two-state case if the intersection of the core of agents' capacities is non-empty; Pareto-optima may then be fully characterized in the two-agent, two-state case. This comonotonicity result does not generalize to more than two states as we show with a counter-example. Finally, if there is no-aggregate risk, we show that non-empty core intersection is enough to guarantee that optimal allocations are full-insurance allocation. This result does not require convexity of preferences.

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