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We characterize the possibility 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, quasilinear preferences for the players with one relaxation - one of the players is subject to a publicly-known budget constraint. We show that the space includes two types of mechanisms: VCG and dictatorial mechanisms. Furthermore when it is publicly known that the budgeted player is not constrained by his budget, VCG uniquely fulfills the basic properties of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal. When it is publicly known that the budgeted player is constrained on all bundles then only a dictatorial solution will fulfill the above properties. Moreover when it is publicly known that the budgeted player is constrained on the largest bundle there are preferences under which the VCG mechanism uniquely fulfills these properties. [ABSTRACT FROM AUTHOR]

We study multi-unit combinatorial auctions with multi-minded buyers. We provide two deterministic, efficient maximizing, incentive compatible mechanisms that improve upon the known algorithms for the problem (Bartal et al., Proceedings of the 9th Conference on Theoretical Aspects of Rationality and Knowledge TARK IX, pp. 72-87, ). The first mechanism is an online mechanism for a setting in which buyers arrive one-by-one in an online fashion. We then design an offline mechanism with better performance guarantees based on the online mechanism. We complement the results by lower bounds that show that the performance of our mechanisms is close to optimal. The results are based on an online primal-dual approach that was used extensively recently and reveals the underlying structure of the problem. [ABSTRACT FROM AUTHOR]