Computational Aspects of Extending the Shapley Value to Coalitional Games with Externalities

Until recently, computational aspects of the Shapley value were only studied under the assumption that there are no externalities from coalition formation, i.e., that the value of any coalition is independent of other coalitions in the system. However, externalities play a key role in many real-life situations and have been extensively studied in the game-theoretic and economic literature. In this paper, we consider the issue of computing extensions of the Shapley value to coalitional games with externalities proposed by Myerson [21], Pham Do and Norde [23], and McQuillin [17]. To facilitate efficient computation of these extensions, we propose a new representation for coalitional games with externalities, which is based on weighted logical expressions. We demonstrate that this representation is fully expressive and, sometimes, exponentially more concise than the conventional partition function game model. Furthermore, it allows us to compute the aforementioned extensions of the Shapley value in time linear in the size of the input

Generalizing Boolean Satisfiability II: Theory

This is the second of three planned papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal is to define a representation in which this structure is apparent and can easily be exploited to improve computational performance. This paper presents the theoretical basis for the ideas underlying ZAP, arguing that existing ideas in this area exploit a single, recurring structure in that multiple database axioms can be obtained by operating on a single axiom using a subgroup of the group of permutations on the literals in the problem. We argue that the group structure precisely captures the general structure at which earlier approaches hinted, and give numerous examples of its use. We go on to extend the Davis-Putnam-Logemann-Loveland inference procedure to this broader setting, and show that earlier computational improvements are either subsumed or left intact by the new method. The third paper in this series discusses ZAPs implementation and presents experimental performance results

Beyond the literal meaning of words in children with klinefelter syndrome: two case studies

Literature on children with Klinefelter Syndrome (KS) points to general linguistic difficulties in both comprehension and production among other cognitive functions, and in the majority of cases, these coexist with an intellectual level within the norms. In these conditions, children having language delay generally engage in language therapy and are systematically monitored across ages. In this article, we present the profiles of two children with KS (47, XXY), aged 9.1 (Child S) and 13 (Child D), whose language development was assessed as adequate at age 3, and for this reason, did not receive any language treatment. At the present stage, their IQ, as measured by Wechsler Scales (Child S: 92; Child D: 101), is within the norm, but they both present marked weaknesses in pragmatic skills such as figurative language comprehension. The analysis of these two cases points to the need to go beyond global indexes of verbal abilities, as the same global index may mask a wide diversification of individual profiles. In addition, this study underlines the importance of monitoring the developmental trajectories of children like Child D and Child S, because weaknesses in pragmatic skills that are relevant for both academic achievement and social adaptation could emerge at later stages

New Discrete States in Two-Dimensional Supergravity

Two-dimensional string theory is known to contain the set of discrete states that are the SU(2) multiplets generated by the lowering operator of the SU(2) current algebra.Their structure constants are defined by the area preserving diffeomorphisms in two dimensions. We show that the interaction of $d=2$ superstrings with the superconformal ghosts enlarges the algebra of dimension 1 currents and hence the new discrete states appear. These new states are the SU(N) multiplets, if the algebra includes the currents of ghost numbers from -N to N-2, not related by the picture-changing. We compute the structure constants of these new discrete states for N=3 and express them in terms of SU(3) Clebsch-Gordan coefficients,relating their operator algebra to the volume preserving diffeomorphisms in d=3. For general N, the algebra is conjectured to be isomorphic to SDiff(N). This points at possible holographic relations between 2d superstrings and field theories in higher dimensions.Comment: 22 pages; typos corrected, 2 references adde

Data optimizations for constraint automata

Constraint automata (CA) constitute a coordination model based on finite automata on infinite words. Originally introduced for modeling of coordinators, an interesting new application of CAs is implementing coordinators (i.e., compiling CAs into executable code). Such an approach guarantees correctness-by-construction and can even yield code that outperforms hand-crafted code. The extent to which these two potential advantages materialize depends on the smartness of CA-compilers and the existence of proofs of their correctness. Every transition in a CA is labeled by a "data constraint" that specifies an atomic data-flow between coordinated processes as a first-order formula. At run-time, compiler-generated code must handle data constraints as efficiently as possible. In this paper, we present, and prove the correctness of two optimization techniques for CA-compilers related to handling of data constraints: a reduction to eliminate redundant variables and a translation from (declarative) data constraints to (imperative) data commands expressed in a small sequential language. Through experiments, we show that these optimization techniques can have a positive impact on performance of generated executable code