  Advances in computational optimization allow for the organization of large
combinatorial markets. We aim for allocations and competitive equilibrium
prices, i.e. outcomes that are in the core. The research is motivated by the
design of environmental markets, but similar problems appear in energy and
logistics markets or in the allocation of airport time slots. Budget
constraints are an important concern in many of these markets. While the
allocation problem in combinatorial exchanges is already NP-hard with payoff-
maximizing bidders, we find that the allocation and pricing problem becomes
even $\Sigma_2^p$-hard if buyers are financially constrained. We introduce
mixed integer bilevel linear programs (MIBLP) to compute core prices, and
propose pricing functions based on the least core if the core is empty. We also
discuss restricted but simpler cases and effective computational techniques for
the problem. In numerical experiments we show that in spite of the
computational hardness of these problems, we can hope to solve practical
problem sizes, in particular if we restrict the size of the coalitions
considered in the core computations.
