While the focus of mainstream economic analysis of liability rules remains on negligence liability, recently some legal scholars have argued for the sharing of liability. In this paper, our first objective is contribute to the debate regarding the desirability of the sharing of liability for the accident loss. To this end, we study the implications of various approaches toward liability assignment for the existence and efficiency of equilibria. In particular, we analyze the proposal of Calabresi and Cooper (1996). Contrary to what is suggested in the literature, we show that the sharing of liability when parties are either both negligent or both non-negligent does not threaten the existence of equilibria. Moreover, it does not dilute the incentives for the parties to take the due care. Our second objective is to extend the efficiency analysis beyond Shavell (1980, 1987) and Miceli (1997), to search for the second-best liability rules. We show that each of the standard liability rules fails to be efficient even from a second-best perspective. Furthermore, we show that second-best efficiency requires loss sharing between non-negligent parties. As corollaries to our main results, we reexamine some of the existing claims regarding the existence and efficiency of equilibria under liability rules.