Two-Outcome dictatorial mechanisms in constrained combinatorial auctions

We study the limitations of the general space of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal combinatorial auctions in a model with two players and two nonidentical items, Our model has multidimensional types, private values, nonnegative prices, quasilinear preferences for players with one relaxation -one of the players is subject to publicly-known budget constraints. The study concludes that the space described above includes dictatorial mechanisms even if only a single player is subject to publicly-known budget constraints, Moreover we show that if it is publicly known that the player's budget restricts his ability to pay then for mechanisms with two possible outcomes there are two families of dictatorial mechanisms that uniquely fulfill the properties of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto optimal.