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Sensitivity of computer support game algorithms of safe ship control

Józef Lisowski (2013)

International Journal of Applied Mathematics and Computer Science

The paper investigates the sensitivity of safe ship control to inaccurate data from the ARPA anti-collision radar system and to changes in the process control parameters. The system structure of safe ship control in collision situations and computer support programmes exploring information from the ARPA anti-collision radar are presented. Sensitivity characteristics of the multistage positional non-cooperative and cooperative game and kinematics optimization control algorithms are determined through...

Separability by semivalues modified for games with coalition structure

Rafael Amer, José Miguel Giménez (2009)

RAIRO - Operations Research

Two games are inseparable by semivalues if both games obtain the same allocation whatever semivalue is considered. The problem of separability by semivalues reduces to separability from the null game. For four or more players, the vector subspace of games inseparable from the null game by semivalues contains games different to zero-game. Now, for five or more players, the consideration of a priori coalition blocks in the player set allows us to reduce in a significant way the dimension of the vector subspace...

Serial cost sharing

Elena Yanovskaya (2006)

Banach Center Publications

A new axiomatization of the serial method for heterogeneous cost sharing problems is given. One of the axioms is common ordinality. It requires invariance of the method w.r.t. common ordinal transformations of individual utilities.

Seven Proofs for the Subadditivity of Expected Shortfall

Paul Embrechts, Ruodu Wang (2015)

Dependence Modeling

Subadditivity is the key property which distinguishes the popular risk measures Value-at-Risk and Expected Shortfall (ES). In this paper we offer seven proofs of the subadditivity of ES, some found in the literature and some not. One of the main objectives of this paper is to provide a general guideline for instructors to teach the subadditivity of ES in a course. We discuss the merits and suggest appropriate contexts for each proof.With different proofs, different important properties of ES are...

Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator

Antonio Attalienti, Ioan Rasa (2008)

Czechoslovak Mathematical Journal

The paper is devoted to a careful analysis of the shape-preserving properties of the strongly continuous semigroup generated by a particular second-order differential operator, with particular emphasis on the preservation of higher order convexity and Lipschitz classes. In addition, the asymptotic behaviour of the semigroup is investigated as well. The operator considered is of interest, since it is a unidimensional Black-Scholes operator so that our results provide qualitative information on the...

Signed Chip Firing Games and symmetric Sandpile Models on the cycles

Robert Cori, Thi Ha Duong Phan, Thi Thu Huong Tran (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We investigate the Sandpile Model and Chip Firing Game and an extension of these models on cycle graphs. The extended model consists of allowing a negative number of chips at each vertex. We give the characterization of reachable configurations and of fixed points of each model. At the end, we give explicit formula for the number of their fixed points.

Simple equilibria in finite games with convexity properties

Tadeusz Radzik, Piotr Więcek (2015)

Applicationes Mathematicae

This review paper gives a characterization of non-coalitional zero-sum and non-zero-sum games with finite strategy spaces and payoff functions having some concavity or convexity properties. The characterization is given in terms of the existence of two-point Nash equilibria, that is, equilibria consisting of mixed strategies with spectra consisting of at most two pure strategies. The structure of such simple equilibria is discussed in various cases. In particular, many of the results discussed can...

Simple games in Łukasiewicz calculus and their cores

Petr Cintula, Tomáš Kroupa (2013)

Kybernetika

We propose a generalization of simple coalition games in the context of games with fuzzy coalitions. Mimicking the correspondence of simple games with non-constant monotone formulas of classical logic, we introduce simple Łukasiewicz games using monotone formulas of Łukasiewicz logic, one of the most prominent fuzzy logics. We study the core solution on the class of simple Łukasiewicz games and show that cores of such games are determined by finitely-many linear constraints only. The non-emptiness...

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