Optimal Multi-parameter Auction Design

This thesis studies the design of Bayesian revenue-optimal auctions for a class of problems in which buyers have general (non-linear and multi-parameter) preferences. This class includes the classical linear single-parameter problem considered by Myerson (1981), for which he provided a simple characterization of the optimal mechanism, leading to numerous applications in theory and practice. However, for fully general preferences no generic and practical solution is known (various negative computational or structural results exist for special cases), even for the problem of designing a mechanism for a single agent. With general preferences, the optimal mechanism can be complex and impractical. This the-sis identifies key conditions implying that the optimal mechanism is practical. Our main results are different in that they identify different conditions implying different notions of practicality, but are all similar in adopting a modular view to the problem that separates the task of designing a solution for the single-agent problem as the main module, from the task of combining these modules to form an optimal multi-agent mechanism. First, for multi-parameter linear settings, we specify a large class of distributions over values that implies that the optimal single-agent mechanism is posted pricing, and the optimal multi-agent mechanism maximizes virtual values for players ’ favorite items. When agents are identical, the mechanism becomes the second price 4auction with reserve for favorite items. Second, and more generally, we specify a condition called revenue-linearity, defined beyond multi-parameter linear settings, that implies that optimizing agents ’ marginal revenue maximizes revenue. Finally, adopting efficient computability as the notion of practicality, we show that for any setting in which single-agent solutions are efficiently computable, multi-agent solutions are also computable