This paper addresses a problem in axiomatic bargaining, which is a natural variation of the classical models of Nash and Kalai Smorodinsky. Departure from the convexity assumption is justi ed by situations where probability mixture of pure outcomes cannot be implemented. Applications of such problems concern integer allocations of a homogeneous product between two agents, and the problem of fai...

A nonparametric statistical model of small di€usion type is compared with its discretization by a stochastic Euler di€erence scheme. It is shown that the discrete and continuous models are asymptotically equivalent in the sense of Le Cam's de®ciency distance for statistical experiments, when the discretization step decreases with the noise intensity . Mathematics Subject Classi®cation (1991): P...

We introduce a state-based language for programming dynamically changing networks which consist of processes that communicate asynchronously. For this language we introduce an operational semantics and a notion of observable which includes both partial correctness and absence of deadlock. Our main result is a compositional characterization of this notion of observable for a con uent sub-languag...

Game Logic (GL), introduced in [18], is examined from a game-theoretic perspective. A new semantics for GL is proposed in terms of untyped games which are closely related to extensive game forms of perfect information. An example is given of how GL can be used as a formal model of game situations, and some metatheoretic results are presented in the context of their game-theoretic relevance. 200...

Van der Poorten was supported in part by grants from the Australian Research Council and by a research agreement with Digital Equipment Corporation. 1991 Mathematics subject classi cation: 11J68, 11C20 Our investigations in the 1980’s of Thue’s method yielded determinants that we were only able to analyse successfully in part. We explain the context of our work, recount our experiences, mention...

The criterion for con uence using decreasing diagrams is a generalization of several well-known con uence criteria in abstract rewriting, such as the strong con uence lemma. We give a new proof of the decreasing diagram theorem based on a geometric study of in nite reduction diagrams, arising from unsuccessful attempts to obtain a con uent diagram by tiling with elementary diagrams. 2000 Mathem...

We consider a vector kinetic BGK equation leading to isentropic gas dynamics in the relaxation limit. We prove the existence of a weak solution satisfying a kinetic entropy inequality for any initial data with nite energy. Key-words: isentropic gas dynamics { kinetic BGK model { kinetic entropy Mathematics Subject Classi cation: 35L65, 76N15, 35B35, 82C40 Work partially supported by European TM...

Erd os and Gallai showed that for any simple graph with n vertices and circumference c it holds that |E(G)| ≤ 2 (n−1)c.We extend this theorem to simple binary matroids having no F7-minor by showing that for such a matroid M with circumference c(M)≥ 3 it holds that |E(M)| ≤ 1 2 r(M)c(M). Mathematics Subject Classi cation (2000). Primary 05D15; Secondary 05B35.

We study cooperation structures with the following property: Given any two feasible coalitions with non-empty intersection, its union is a feasible coalition again. These combinatorial structures have a direct relationship with graph communication situations and conference structures à la Myerson. Characterizations of the Myerson value in this context are provided using the concept of basis for...

We study some classes of generalized a¢ ne functions, using a generalized di¤erential. We study some properties and characterizations of these classes and we devise some characterizations of solution sets of optimization problems involving such functions or functions of related classes. Key words: colinvex, colin…ne, generalized di¤erential, optimization problem, protoconvex function, pseudocon...