Combinatorial Auctions with Decreasing Marginal Utilities

In most of microeconomic theory, consumers are assumed to exhibit decreasing marginal utilities. This paper considers combinatorial auctions among such submodular buyers. The valuations of such buyers are placed within a hierarchy of valuations that exhibit no complementarities, a hierarchy that includes also OR and XOR combinations of singleton valuations, and valuations satisfying the gross substitutes property. Those last valuations are shown to form a zero-measure subset of the submodular valuations that have positive measure. While we show that the allocation problem among submodular valuations is NP-hard, we present an efficient greedy 2-approximation algorithm for this case and generalize it to the case of limited complementarities. No such approximation algorithm exists in a setting allowing for arbitrary complementarities. Some results about strategic aspects of combinatorial auctions among players with decreasing marginal utilities are also presented.Comment: To appear in GEB. Preliminary version appeared in EC'0

Iitaka dimension for cycles

We define the Iitaka dimension of a numerical cycle class and develop its theory. We conjecture that the Iitaka dimension is integer-valued, and give some evidence in this direction. We focus on two cases of geometric interest: Schubert cycles on Grassmannians and cycles contracted by morphisms.Comment: 24 page

Algebraic bounds on analytic multiplier ideals

Given a pseudo-effective divisor L we construct the diminished ideal of L, a "continuous" extension of the asymptotic multiplier ideal for big divisors to the pseudo-effective boundary. For most pseudo-effective divisors L the multiplier ideal of the metric of minimal singularities of L is contained in the diminished ideal. We also characterize abundant divisors using the diminished ideal, indicating that in this case the geometric and analytic information should coincide.Comment: 27 pages; v3: corrected several mistake

Crisis management for euro-area banks in central Europe. Bruegel Policy Contribution Issue #14 November 2019

The deep involvement of a number of euro-area banking groups in central and southeastern Europe has benefi tted the host countries and has strengthened the resilience of those banking groups. But this integration has become less close because of post-financial crisis national rules that require banks to hold more capital at home, or other ring-fencing measures. Th ere is a risk integration might be undermined further by bank resolution planning, which is now gathering pace. Regulators and banks will need to decide between two distinct models for crisis resolution, and this choice will redefi ne banking networks. Most effi cient in terms of preserving capital and the close integration of subsidiary operations would be if the Single Resolution Board – the banking union’s central resolution authority – takes the lead for the entire banking group. However, this will require parent banks to hold the subordinated debts of their subsidiaries. Persistent barriers to intra-group capital mobility – or the option for home or host authorities to impose such restrictions – will ultimately render such schemes unworkable. The second model would involve independent local intervention schemes, which European Union countries outside the banking union are likely to call for. Th is will require building capacity in local debt markets, and clarifying creditor hierarchies. Exposure to banking risks will ultimately need to be borne by host-country investors. Bail-in capital issued by subsidiaries to their parents cannot be a substitute because it would expose the home country to fi nancial contagion from the host. To sustain cross-border linkages, banking groups and their supervisors will need to make bank recovery plans more credible, and to strengthen cooperation in resolution colleges (platforms that bring together all relevant parties in resolution planning and execution). Within the banking union there is no justifi cation for the various ring-fencing measures that have impeded the fl ow of capital and liquidity within banking group