This paper studies the effect of limited commitment on sorting when two sides of a frictionless market form pairs to share risk. On each side, agents are identical except for their risk preferences. First, we provide analytical results when transfers do not condition on the history of shocks. More risk-averse agents can commit to larger transfers, as long as their consumption is less risky than their endowment. With sufficiently large idiosyncratic risk and sufficient discounting of the future, matching is positive assortative, unlike under full commitment. Second, we find positive-assortative stable matchings when transfers are history dependent using a numerical algorithm.
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