The paper studies equilibrium sharing of risk among limited number of strategically-behaved agents. We propose a Nash game where agents' strategic sets consist of all possible sharing securities and pricing kernels that are consistent with Arrow-Debreu sharing rules. First, it is shown that the best response problem of each agent admits a unique solution . The risk-sharing Nash equilibrium admits a finite-dimensional characterisation and it is proved to  be unique in the case of two agents. In Nash risk-sharing equilibrium agents choose to share random endowments that are different than their actual ones , and the shared securities are endogenously bounded, implying (amongst other things) loss of efficiency. In addition, an analysis regarding extremely risk tolerant agents indicates that they profit more from the Nash risk-sharing equilibrium as compared to the Arrow-Debreu one.
The large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. This paper proposes a game where agents' strategic sets consist of all possible sharing securities and pricing kernels that are consistent with Arrow-Debreu sharing rules. First, it is shown that agents' best response problems have unique solutions, even when the underlying probability space is infinite . The risk-sharing Nash equilibrium admits a finite-dimensional characterisation and it is proved to exist for general number of agents and be unique in the two-agent game. In equilibrium, agents choose to declare beliefs on future random outcomes different from their actual probability assessments , and the risk-sharing securities are endogenously bounded, implying (amongst other things) loss of efficiency. In addition, an analysis regarding extremely risk tolerant agents indicates that they profit more from the Nash risk-sharing equilibrium as compared to the Arrow-Debreu one.
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paper studies equilibrium sharing of risk among limited number of strategically-behaved agents. We propose a Nash
large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. This paper proposes a
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the best response problem of each agent admits a unique solution
agents' best response problems have unique solutions, even when the underlying probability space is infinite
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exist for general number of agents and
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case of two agents. In Nash risk-sharing equilibrium
two-agent game. In equilibrium,
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share random endowments that are different than their actual ones
declare beliefs on future random outcomes different from their actual probability assessments
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shared
risk-sharing