On the incentive properties of multi-item auctions

In a market of indivisible obects where a buyer consumes at most one object, the buyer-optimal auction is a multi-item generalization of Vickrey's second-price auction. If the optimal auction is formulated as a strategic game, it is well-known that it satisfies good incentive properties, i.e., the honest strategy profile is a Nash equilibrium, a unique perfect equilibrium and a dominant strategy equilibrium. For each of the three incentive properties, it is shown that the optimal auction is a unique auction satisfying the property. The uniqueness results are derived in a general setting with budget constraints and non-linear utilities.