Before revision:  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.
After revision:  The risk-sharing Nash equilibrium admits a finite-dimensional characterisation and it is proved to be unique in the two-agent game. In 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.