Associated consistency and values for TU games

In the framework of the solution theory for cooperative transferable utility games, Hamiache axiomatized the well-known Shapley value as the unique one-point solution verifying the inessential game property, continuity, and associated consistency. The purpose of this paper is to extend Hamiache's axiomatization to the class of efficient, symmetric, and linear values, of which the Shapley value is the most important representative. For this enlarged class of values, explicit relationships to the Shapley value are exploited in order to axiomatize such values with reference to a slightly adapted inessential game property, continuity, and a similar associated consistency. The latter axiom requires that the solutions of the initial game and its associated game (with the same player set, but a different characteristic function) coincide

A potential approach to solutions for set games

Concerning the solution theory for set games, the paper introduces a new solution by allocating, to any player, the items (taken from an universe) that are attainable for the player, but can not be blocked (by any coalition not containing the player). The resulting value turns out to be an utmost important concept for set games to characterize the family of set game solutions that possess a so-called potential representation (similar to the potential approaches applied in both physics and cooperative game theory). An axiomatization of the new value, called Driessen--Sun value, is given by three properties, namely one type of an efficiency property, the substitution property and one type of a monotonocity property

A uniform approach to semi-marginalistic values for set games

Concerning the solution theory for set games, the paper focuses on a family of solutions, each of which allocates to any player some type of marginalistic contribution with respect to any coalition containing the player. Here the marginalistic contribution may be interpreted as an individual one, or a coalitionally one. For any value of the relevant family, an axiomatization is given by three properties, namely one type of an efficiency property, the substitution property and one type of a monotonocity property. We present two proof techniques, each of which is based on the decomposition of any arbitrary set game into a union of either simple set games or elementary set games, the solutions of which are much easier to determine. A simple respectively elementary set game is associated with an arbitrary, but fixed item of the universe respectively coalition

Incident Analysis & Digital Forensics in SCADA and Industrial Control Systems

SCADA and industrial control systems have been traditionally isolated in physically protected environments. However, developments such as standardisation of data exchange protocols and increased use of IP, emerging wireless sensor networks and machine-to-machine communication mean that in the near future related threat vectors will require consideration too outside the scope of traditional SCADA security and incident response. In the light of the significance of SCADA for the resilience of critical infrastructures and the related targeted incidents against them (e.g. the development of stuxnet), cyber security and digital forensics emerge as priority areas. In this paper we focus on the latter, exploring the current capability of SCADA operators to analyse security incidents and develop situational awareness based on a robust digital evidence perspective. We look at the logging capabilities of a typical SCADA architecture and the analytical techniques and investigative tools that may help develop forensic readiness to the level of the current threat environment requirements. We also provide recommendations for data capture and retention

Do micro brown dwarf detections explain the galactic dark matter?

Context: The baryonic dark matter dominating the structures of galaxies is widely considered as mysterious, but hints for it have been in fact detected in several astronomical observations at optical, infrared, and radio wavelengths. We call attention to the nature of galaxy merging, the observed rapid microlensing of a quasar, the detection of "cometary knots" in planetary nebulae, and the Lyman-alpha clouds as optical phenomena revealing the compact objects. Radio observations of "extreme scattering events" and "parabolic arcs" and microwave observations of "cold dust cirrus" clouds are observed at 15 - 20 K temperatures are till now not considered in a unifying picture. Aims: The theory of gravitational hydrodynamics predicts galactic dark matter arises from Jeans clusters that are made up of almost a trillion micro brown dwarfs (mBDs) of earth weight. It is intended to explain the aforementioned anomalous observations and to make predictions within this framework. Methods: We employ analytical isothermal modeling to estimate various effects. Results: Estimates of their total number show that they comprise enough mass to constitute the missing baryonic matter. Mysterious radio events are explained by mBD pair merging in the Galaxy. The "dust" temperature of cold galaxy halos arises from a thermostat setting due to a slow release of latent heat at the 14 K gas to solid transition at the mBD surface. The proportionality of the central black hole mass of a galaxy and its number of globular clusters is explained. The visibility of an early galaxy at redshift 8.6 is obvious with most hydrogen locked up in mBDs. Conclusions: Numerical simulations of various steps would further test the approach. It looks promising to redo MACHO searches against the Magellanic clouds.Comment: 12 pages A&A tex, 3 pdf figure

The Mass Function of Primordial Rogue Planet MACHOs in quasar nanolensing

The recent Sumi et al (2010, 2011) detection of free roaming planet mass MACHOs in cosmologically significant numbers recalls their original detection in quasar microlening studies (Schild 1996, Colley and Schild 2003). We consider the microlensing signature of such a population, and find that the nano-lensing (microlensing) would be well characterized by a statistical microlensing theory published previously by Refsdal and Stabel (1991). Comparison of the observed First Lens microlensing amplitudes with the theoretical prediction gives close agreement and a methodology for determining the slope of the mass function describing the population. Our provisional estimate of the power law exponent in an exponential approximation to this distribution is $2.98^{+1.0}_{-0.5}.$ where a Salpeter slope is 2.35.Comment: 12 pages, 1 figur

A multiplicative potential approach to solutions for cooperative TU-games

Concerning the solution theory for cooperative games with transferable utility, it is well-known that the Shapley value is the most appealing representative of the family of (not necessarily efficient) game-theoretic solutions with an additive potential representation. This paper introduces a new solution concept, called Multiplicativily Proportional ($MP$) value, that can be regarded as the counterpart of the Shapley value if the additive potential approach to the solution theory is replaced by a multiplicative potential approach in that the difference of two potential evaluations is replaced by its quotient. One out of two main equivalence theorems states that every solution with a multiplicative potential representation is equivalent to this specifically chosen efficient value in that the solution of the initial game coincides with the $MP$ value of an auxiliary game. The associated potential function turns out to be of a multiplicative form (instead of an additive form) with reference to the worth of all the coalitions. The second equivalence theorem presents four additional characterizations of solutions that admit a multiplicative potential representation, e.g., preservation of discrete ratios or path independence

Matrix approach to the Shapley value and dual similar associated consistency

Replacing associated consistency in Hamiache's axiom system by dual similar associated consistency, we axiomatize the Shapley value as the unique value verifying the inessential game property, continuity and dual similar associated consistency. Continuing the matrix analysis for Hamiache's axiomatization of the Shapley value, we construct the dual similar associated game and introduce the dual similar associated transformation matrix $M_\lambda^{DSh}$ as well. In the game theoretic framework we show that the dual game of the dual similar associated game is Hamiache's associated game of the dual game. For the purpose of matrix analysis, we derive the similarity relationship $M_\lambda^{DSh}=QM_\lambda Q^{-1}$ between the dual similar associated transformation matrix $M_\lambda^{DSh}$ and associated transformation matrix $M_\lambda$ for Hamiache's associated game, where the transformation matrix $Q$ represents the duality operator on games. This similarity of matrices transfers associated consistency into dual similar associated consistency, and also implies the inessential property for the limit game of the convergent sequence of repeated dual similar associated games. We conclude this paper with three tables summarizing all matrix results