On the coincidence of the Mas-Colell bargaining set and the core

In this paper we prove that the Mas-Colell bargaining set coincides with the core for three-player balanced and superadditive cooperative games. This is no longer true without the superadditivity condition or for games with more than three-players. Furthermore, under the same assumptions, the coincidence between the Mas-Collel and the individual rational bargaining set (Vohra (1991)) is revealed. Keywords: Cooperative game, Mas-Colell bargaining set, balancedness, individual rational bargaining set. JEL classi fication: C71, D63, D71.

Manipulation via endowments in exchange markets with indivisible goods

We consider exchange markets with heterogeneous indivisible goods. We are interested in exchange rules that are efficient and immune to manipulations via endowments (either with respect to hiding or destroying part of the endowment or transferring part of the endowment to another trader). We consider three manipulability axioms: hiding-proofness, destruction-proofness, and transfer-proofness. We prove that no rule satisfying efficiency and hiding-proofness (which implies individual rationality) exists. For two-agent exchange markets with separable and responsive preferences, we show that efficient, individually rational, and destruction-proof rules exist. However, for separable preferences, no rule satisfies efficiency, individual rationality, and destruction-proofness. In the case of transfer-proofness the compatibility with efficiency and individual rationality for the two-agent case extends to the unrestricted domain. For exchange markets with separable preferences and more than two agents no rule satisfies efficiency, individual rationality, and transfer-proofness.

A One-Shot Prisoners Dilemma with Procedural Utility

This article introduces a model of rationality that combines procedural utility over actions with consequential utility over payoffs. It applies the model to the Prisoners Dilemma and shows that empirically observed cooperative behaviors can be rationally explained by a procedural utility for cooperation. The model characterizes the situations in which cooperation emerges as a Nash equilibrium. When rational individuals are not solely concerned by the consequences of their behavior but also care for the process by which these consequences are obtained, there is no one single rational solution to a Prisoners Dilemma. Rational behavior depends on the payoffs at stake and on the procedural utility of individuals. In this manner, this model of procedural utility reflects how ethical considerations, social norms or emotions can transform a game of consequences.

Additive utility with intransitive indifference and without independence: A homogeneous case

In the homogeneous case of one type of goods or objects, we prove theexistence of an additive utility function without assuming transitivityof indifference and independence. The representation reveals a positivefactor smaller than 1 that infuences rational choice beyond the utilityfunction and explains departures from these standard axioms of utilitytheory (factor equals to 1).

An axiomatization of the prekernel of nontransferable utility games

We characterize the prekernel of NTU games by means of consistency,converse consistency, and five axioms of the Nash type on bilateral problems.The intersection of the prekernel and the core is also characterized with thesame axioms over the class of games where the core is nonempty.

A one-shot Prisoners’ Dilemma with procedural utility

This article introduces a model of rationality that combines procedural utility over actions with consequential utility over payoffs. It applies the model to the Prisoners Dilemma and shows that empirically observed cooperative behaviors can be rationally explained by a procedural utility for cooperation. The model characterizes the situations in which cooperation emerges as a Nash equilibrium. When rational individuals are not solely concerned by the consequences of their behavior but also care for the process by which these consequences are obtained, there is no one single rational solution to a Prisoners Dilemma. Rational behavior depends on the payoffs at stake and on the procedural utility of individuals. In this manner, this model of procedural utility reflects how ethical considerations, social norms or emotions can transform a game of consequences.

A process approach to the utility for gambling

This paper argues that any specific utility or disutility for gamblingmust be excluded from expected utility because such a theory is consequentialwhile a pleasure or displeasure for gambling is a matter of process, notof consequences. A (dis)utility for gambling is modeled as a process utilitywhich monotonically combines with expected utility restricted to consequences.This allows for a process (dis)utility for gambling to be revealed. Asan illustration, the model shows how empirical observations in the Allaisparadox can reveal a process disutility of gambling. A more general modelof rational behavior combining processes and consequences is then proposedand discussed.

The set of undominated imputations and the core: an axiomatic approach

This paper provides an axiomatic framework to compare the D-core (the set of undominatedimputations) and the core of a cooperative game with transferable utility. Theorem1 states that the D-core is the only solution satisfying projection consistency, reasonableness (from above), (*)-antimonotonicity, and modularity. Theorem 2 characterizes the core replacing (*)-antimonotonicity by antimonotonicity. Moreover, these axioms alsocharacterize the core on the domain of convex games, totally balanced games, balancedgames, and superadditive games

The set of undominated imputations and the core: an axiomatic approach

This paper provides an axiomatic framework to compare the D-core (the set of undominatedimputations) and the core of a cooperative game with transferable utility. Theorem1 states that the D-core is the only solution satisfying projection consistency, reasonableness (from above), (*)-antimonotonicity, and modularity. Theorem 2 characterizes the core replacing (*)-antimonotonicity by antimonotonicity. Moreover, these axioms alsocharacterize the core on the domain of convex games, totally balanced games, balancedgames, and superadditive games

GSVA: gene set variation analysis for microarray and RNA-seq data

Gene set enrichment (GSE) analysis is a popular framework for condensing information from gene expression profiles into a pathway or signature summary. The strengths of this approach over single gene analysis include noise and dimension reduction, as well as greater biological interpretability. As molecular profiling experiments move beyond simple case-control studies, robust and flexible GSE methodologies are needed that can model pathway activity within highly heterogeneous data sets. To address this challenge, we introduce Gene Set Variation Analysis (GSVA), a GSE method that estimates variation of pathway activity over a sample population in an unsupervised manner. We demonstrate the robustness of GSVA in a comparison with current state of the art sample-wise enrichment methods. Further, we provide examples of its utility in differential pathway activity and survival analysis. Lastly, we show how GSVA works analogously with data from both microarray and RNA-seq experiments. GSVA provides increased power to detect subtle pathway activity changes over a sample population in comparison to corresponding methods. While GSE methods are generally regarded as end points of a bioinformatic analysis, GSVA constitutes a starting point to build pathway-centric models of biology. Moreover, GSVA contributes to the current need of GSE methods for RNA-seq data. GSVA is an open source software package for R which forms part of the Bioconductor project and can be downloaded at http://www.bioconductor.org.

Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

Gene Set Analysis for improving genetic association studies

Introduction. Genetic epidemiology is focused on the study of the genetic causes that determine health and diseases in populations. To achieve this goal a common strategy is to explore differences in genetic variability between diseased and nondiseased individuals. Usual markers of genetic variability are single nucleotide polymorphisms (SNPs) which are changes in just one base in the genome. The usual statistical approach in genetic epidemiology study is a marginal analysis, where each SNP is analyzed separately for association with the phenotype. Motivation. It has been observed, that for common diseases the single-SNP analysis is not very powerful for detecting genetic causing variants. In this work, we consider Gene Set Analysis (GSA) as an alternative to standard marginal association approaches. GSA aims to assess the overall association of a set of genetic variants with a phenotype and has the potential to detect subtle effects of variants in a gene or a pathway that might be missed when assessed individually. Objective. We present a new optimized implementation of a pair of gene set analysis methodologies for analyze the individual evidence of SNPs in biological pathways. We perform a simulation study for exploring the power of the proposed methodologies in a set of scenarios with different number of causal SNPs under different effect sizes. In addition, we compare the results with the usual single-SNP analysis method. Moreover, we show the advantage of using the proposed gene set approaches in the context of an Alzheimer disease case-control study where we explore the Reelin signal pathway.

Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

The Barcelonnettes: an example of network-entrepreneurs in XIX century Mexico. An explanation based on a theory of bounded rational choice with social embeddedness

A theory of network-entrepreneurs or "spin-off system" is presented in this paper for the creation of firms based on the community’s social governance. It is argued that firm’s capacity for accumulation depends on the presence of employees belonging to the same social/ethnic group with expectations of "inheriting" the firm and becoming entrepreneurs once they have been selected for their merits and loyalty towards their patrons. Such accumulation is possible because of the credibility of the patrons’ promises of supporting newcomers due to high social cohesion and specific social norms prevailing in the community. This theory is exemplified through the case of the Barcelonnettes, a group of immigrants from the Alps in the South of France (Provence) who came to Mexico in the XIX Century.

On the set of subrings wich are directed unions of Artinian subrings

The paper contributes to the investigation of zero-dimensional rings which can be written as a directed union of Artinian subrings. We give conditions on DU(R) in order to be nonempty.