This paper examines how cooperation in an insurance game depends on risk preferences and the riskiness of income. It considers a dynamic game where commitment is limited, and characterizes the level of cooperation as measured by the reciprocal of the discount factor above which perfect risk sharing is self-enforcing. When agents face no aggregate risk, there is more cooperation, if (i) the utility function is more concave, and if (ii) income is more risky considering a mean-preserving spread or an SSD deterioration. However, (ii) no longer holds when insurance can only be incomplete, because of the interplay of idiosyncratic and aggregate risk. In the case of exponential (isoelastic) utility, cooperation depends positively on both the coefficient of absolute (relative) risk aversion and the standard deviation (coefficient of variation), and is independent of mean income. This paper also relates the level of cooperation to informal insurance transfers and the smoothness of consumption when perfect risk sharing is not achieved.