Bid and Guess: A Nested Mechanism for King Solomon's Dilemma

In this paper we propose a mechanism to resolve King Solomon’s dilemma about allocating an indivisible good at no cost to the participating agents. A distinctive feature of our mechanism is the design of a two-part contest that makes the agents guess each other’s bids in a second-price auction. The accuracy of an agent’s guess of the other agent’s bid endogenously determines how much she pays for participating in the contest. The truthfully bidding Bayesian-Nash equilibrium of the contesting game results in a reduced game, which has a unique and strict Bayesian-Nash equilibrium that implements the efficient outcome.