Effective risk aversion in thin risk-sharing markets

We consider thin incomplete financial markets, where traders with heterogeneous preferences and risk exposures have motive to behave strategically regarding the demand schedules they submit, thereby impacting prices and allocations. We argue that traders relatively more exposed to the market portfolio tend to behave in a more risk tolerant manner. Noncompetitive equilibrium prices and allocations result as an outcome of a game among traders. General sufficient conditions for existence and uniqueness of such equilibrium are provided, with extensive analysis of two-trader transactions. Even though strategic behavior causes inefficient social allocations, traders with sufficiently high risk tolerance and/or high initial exposure to tradable securities obtain more utility gain in the noncompetitive equilibrium, when compared to the competitive one.