On extensions of the core and the anticore of transferable utility games

We consider several related set extensions of the core and the anticore of games with transferable utility. An efficient allocation is undominated if it cannot be improved, in a specific way, by sidepayments changing the allocation or the game. The set of all such allocations is called the undominated set, and we show that it consists of finitely many polytopes with a core-like structure. One of these polytopes is the L1-center, consisting of all efficient allocations that minimize the sum of the absolute values of the excesses. The excess Pareto optimal set contains the allocations that are Pareto optimal in the set obtained by ordering the sums of the absolute values of the excesses of coalitions and the absolute values of the excesses of their complements. The L1-center is contained in the excess Pareto optimal set, which in turn is contained in the undominated set. For three-person games all these sets coincide. These three sets also coincide with the core for balanced games and with the anticore for antibalanced games. We study properties of these sets and provide characterizations in terms of balanced collections of coalitions. We also propose a single-valued selection from the excess Pareto optimal set, the min-prenucleolus, which is defined as the prenucleolus of the minimum of a game and its dual.Transferable utility game; core; anticore; core extension; min-prenucleolus

Designating market maker behaviour in Limit Order Book markets

Financial exchanges provide incentives for limit order book (LOB) liquidity provision to certain market participants, termed designated market makers or designated sponsors. While quoting requirements typically enforce the activity of these participants for a certain portion of the day, we argue that liquidity demand throughout the trading day is far from uniformly distributed, and thus this liquidity provision may not be calibrated to the demand. We propose that quoting obligations also include requirements about the speed of liquidity replenishment, and we recommend use of the Threshold Exceedance Duration (TED) for this purpose. We present a comprehensive regression modelling approach using GLM and GAMLSS models to relate the TED to the state of the LOB and identify the regression structures that are best suited to modelling the TED. Such an approach can be used by exchanges to set target levels of liquidity replenishment for designated market makers

Reservations to Multilateral Treaties: How International Legal Doctrine Reflects World Vision

When a state makes a reservation to an existing or proposed multilateral treaty, it takes exception to one or more provisions of that treaty. A valid reservation alters the state\u27s rights and obligations under the treaty with respect to the objectionable portion. Although reservations appear to be merely a legal technicality, a last-minute accommodation after complicated multilateral negotiations, the doctrine of reservations in fact strikes at the heart of the concept of a multilateral convention. The doctrine pits an individual state\u27s desire to depart from the terms of the treaty against the general agreement of all parties to be bound equally by the terms of a common document. By examining the evolution of the doctrine of reservations in this century, this Comment will explore how the successive versions of the doctrine reflect the changing conception of multilateral conventions, and will illustrate how a tiny nugget of treaty law provides a battleground for the clash between two basic opposing visions of the world: a world composed of autonomous states versus an integrated world order. This analysis will show how each version of the doctrine of reservations represents a new balance struck between two competing conceptions of multilateral conventions, each of which is based on a particular vision of world society and the international legal order. Part I describes the methodology of this analysis and outlines the nature of pure subjective and purposive views of the validity of reservations; it then describes how each of these views suggests particular visions of multilateral treaties and of international relations. Part II analyzes each of the five versions of the doctrine of reservations which have prevailed during this century and in each case derives the conflicting conceptions of multilateral treaties that each new version of the doctrine reveals. Finally. Part III, with the help of the graphical analysis presented in the Appendix, summarizes the conclusions of Part II and speculates on the implications of this analysis beyond the realm of the law of reservations

Habit, Story, Delight: Essential Tools for the Public Service Advocate

It is truly a joy to be at Washington University School of Law. I am especially honored to visit Washington University, whose clinical faculty is second to none in their national contributions to the clinical law teaching movement. From my point of view, a student-centered law school with a client-centered clinic is truly nirvana. This speech is a compilation of stories and reflections about the life of a public service lawyer. I imagine that past speakers came to this series to exhort you to join the ranks of public interest lawyers. I am not here for that purpose. Instead, I want to tell you about the life of a public service lawyer and to offer you solutions that some of my colleagues and I have developed for the challenges encountered in the daily life of a public service lawyer. I use the term public service lawyer to describe lawyers who represent individual, often poor clients. Such lawyers usually represent a great number of clients, unless they are, like me, lucky enough to be a clinical teacher (in which case they may represent a smaller number of clients with the help of very able law students). I would like to offer you some skills that will stand you in good stead for such a career

Habit, Story, Delight: Essential Tools for the Public Service Advocate

This Essay is a compilation of stories and reflections about the life of a public service lawyer