On minimum integer representations of weighted games

We study minimum integer representations of weighted games, i.e., representations where the weights are integers and every other integer representation is at least as large in each component. Those minimum integer representations, if the exist at all, are linked with some solution concepts in game theory. Closing existing gaps in the literature, we prove that each weighted game with two types of voters admits a (unique) minimum integer representation, and give new examples for more than two types of voters without a minimum integer representation. We characterize the possible weights in minimum integer representations and give examples for $t\ge 4$ types of voters without a minimum integer representation preserving types, i.e., where we additionally require that the weights are equal within equivalence classes of voters.Comment: 29 page

Monetary policy in a systemic crisis

This paper examines the monetary policy followed during the current financial crisis from the perspective of the theory of the lender of last resort. It is argued that standard monetary policy measures would have failed because the channels through which monetary policy is implemented depend upon the well functioning of the interbank market. As the crisis developed, liquidity vanished and the interbank market collapsed, central banks had to inject much more liquidity at low interest rates than predicted by standard monetary policy models. At the same time, as the interbank market did not allow for the redistribution of liquidity among banks, central banks had to design new channels for liquidity injection.

An overall perspective on banking regulation

We survey the theory of banking regulation from the general perspective of regulatory theory. Starting by considering the different justifications of financial intermediation, we proceed to identify the market failures that make banking regulation necessary. We then succinctly compare how the analysis of regulation compares in the domains of banking and industrial organization. Finally we analyse why a safety net for banks could be part of banking regulation and how it can be structured in an efficient way.Banking regulation, efficiency, financial stability, banking supervision

Bounds for the Nakamura number

The Nakamura number is an appropriate invariant of a simple game to study the existence of social equilibria and the possibility of cycles. For symmetric quota games its number can be obtained by an easy formula. For some subclasses of simple games the corresponding Nakamura number has also been characterized. However, in general, not much is known about lower and upper bounds depending of invariants on simple, complete or weighted games. Here, we survey such results and highlight connections with other game theoretic concepts.Comment: 23 pages, 3 tables; a few more references adde

Post crisis challenges to bank regulation

The current crisis has swept aside not only the whole of the US investment banking industry but also the consensual perception of banking risks, contagion and their implication for banking regulation. As everyone agrees now, risks where mispriced, they accumulated in neuralgic points of the financial system, and where amplified by procyclical regulation as well as by the instability and fragility of financial institutions. The use of ratings as carved in stone and lack of adequate procedure to swiftly deal with systemic institutions bankruptcy (whether too-big-to-fail, too complex to fail or too-many to fail). The current paper will not deal with the description and analysis of the crisis, already covered in other contributions to this issue will address the critical choice regulatory authorities will face. In the future regulation has to change, but it is not clear that it will change in the right direction. This may occur if regulatory authorities, possibly influenced by public opinion and political pressure, adopt an incorrect view of financial crisis prevention and management. Indeed, there are two approaches to post-crisis regulation. One is the rare event approach, whereby financial crises will occur infrequently, but are inescapable.

Corporate finance and the monetary transmission mechanism

This paper analyzes the transmission mechanisms of monetary policy in a general equilibrium model of securities markets and banking with asymmetric information. Banks' optimal asset/liability policy is such that in equilibrium capital adequacy constraints are always binding. Asymmetric information about banks' net worth adds a cost to outside equity capital, which limits the extent to which banks can relax their capital constraint. In this context monetary policy does not affect bank lending through changes in bank liquidity. Rather, it has the effect of changing the aggregate composition of financing by firms. The model also produces multiple equilibria, one of which displays all the features of a "credit crunch". Thus, monetary policy can also have large effects when it induces a shift from one equilibrium to the other.Asymmetric information, liabilities structure, capital regulation, monetary policy, transmission mechanism

Interbank market integration under asymmetric information

We argue that the main barrier to an integrated international interbank market is the existence of asymmetric information between different countries, which may prevail in spite of monetary integration or successful currency pegging. In order to address this issue, we study the scope for international interbank market integration with unsecured lending when cross-country information is noisy. We find not only that an equilibrium with integrated markets need not always exist, but also that when it does, the integrated equilibrium may coexist with one of interbank market segmentation. Therefore, market deregulation, per se, does not guarantee the emergence of an integrated interbank market. The effect of a repo market which, a priori, was supposed to improve efficiency happens to be more complex: it reduces interest rate spreads and improves upon the segmentation equilibrium, but\ it may destroy the unsecured integrated equilibrium, since the repo market will attract the best borrowers. The introduction of other transnational institutional arrangements, such as multinational banking, correspondent banking and the existence of "too-big-to-fail" banks may reduce cross country interest spreads and provide more insurance against country wide liquidity shocks. Still, multinational banking, as the introduction of repos, may threaten the integrated interbank market equilibrium.Banking theory, asymmetric information, financial integration, interbank markets, diamond-dybvig

An arithmetic Hilbert-Samuel theorem for singular hermitian line bundles and cusp forms

We prove an arithmetic Hilbert-Samuel type theorem for semi-positive singular hermitian line bundles of finite height. In particular, the theorem applies to the log-singular metrics of Burgos-Kramer-K\"uhn. Our theorem is thus suitable for application to some non-compact Shimura varieties with their bundles of cusp forms. As an application, we treat the case of Hilbert modular surfaces, establishing an arithmetic analogue of the classical result expressing the dimensions of spaces of cusp forms in terms of special values of Dedekind zeta functions