Divide and compromise

We introduce two symmetrized versions of the popular divide-and-choose mechanism for the allocation of a collectively owned indivisible good between two agents when monetary compensation is available. Our proposals retain the simplicity of divide-and-choose and correct its ex-post asymmetry. When there is complete information, i.e., agents know each other well, both mechanisms implement in subgame perfect equilibria a unique allocation that would be obtained by a balanced market. The results hold for general continuous preferences that may not be quasi-linear.