An Equilibrium Analysis of Knaster's Fair Division Procedure

In an incomplete information setting, we analyze the sealed bid auction proposed by Knaster (cf. Steinhaus (1948)). This procedure was designed to effi ciently and fairly allocate multiple indivisible items when participants report their valuations truthfully. In equilibrium, players do not follow truthful bidding strategies. We find that, expost, the equilibrium allocation is still effi cient, however, may not be fair. However, on average, participants receive the same outcome they would have received if everyone had reported truthfully — i.e., the mechanism is ex-ante fair.