2018/07/22 by Martin Bichler, Bichler, Martin, Stefan Waldherr +1
Decision Sciences · Economics, Econometrics and Finance · #Auction Theory and Applications #Computer Science and Game Theory (cs.GT) #Economic theories and models #F.2 #FOS: Computer and information sciences #Game Theory and Voting Systems
paper · pdf · doi:10.48550/arxiv.1807.08253
openalex publication_date 2018/07/22 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
Advances in computational optimization allow for the organization of large\ncombinatorial markets. We aim for allocations and competitive equilibrium\nprices, i.e. outcomes that are in the core. The research is motivated by the\ndesign of environmental markets, but similar problems appear in energy and\nlogistics markets or in the allocation of airport time slots. Budget\nconstraints are an important concern in many of these markets. While the\nallocation problem in combinatorial exchanges is already NP-hard with payoff-\nmaximizing bidders, we find that the allocation and pricing problem becomes\neven \Σ2p-hard if buyers are financially constrained. We introduce\nmixed integer bilevel linear programs (MIBLP) to compute core prices, and\npropose pricing functions based on the least core if the core is empty. We also\ndiscuss restricted but simpler cases and effective computational techniques for\nthe problem. In numerical experiments we show that in spite of the\ncomputational hardness of these problems, we can hope to solve practical\nproblem sizes, in particular if we restrict the size of the coalitions\nconsidered in the core computations.\n