Monotonicity properties of the interval solutions and the Dutta-Ray solution for convex interval games

E. B. Yanovskaya; Branzei R.; Tijs S.

?

Monotonicity properties of the interval solutions and the Dutta-Ray solution for convex interval games

P. 249–266.

Yanovskaya E. B., Branzei R., Tijs S.

This paper examines several monotonicity properties of value-type interval solutions on the class of convex interval games and focuses on the Dutta-Ray (DR) solution for such games. Well known properties for the classical DR solution are extended to the interval setting. In particular, it is proved that the interval DR solution of a convex interval game belongs to the interval core of that game and Lorenz dominates each other interval core element. Consistency properties of the interval DR solution in the sense of Davis-Maschler and of Hart-Mas-Colell are verified. An axiomatic characterization of the interval DR solution on the class of convex interval games with the help of bilateral Hart-Mas-Colell consistency and the constrained egalitarianism for two-person interval games is given.

Language: English

Full text

Keywords: Dutta-Ray solution convex game решение Дутта-Рэя выпуклая игра interval game monotonicity интервальная игра монотонность

In book

Collective decision making

Vol. 43: Views from Social Choice and Game Theory. , Dordrecht: Springer, 2010.

Population monotonicity and egalitarianism

Dietzenbacher B., Dogan E., International Journal of Game Theory 2025 Vol. 54 Article 42

This paper identifies the maximal domain of transferable utility games on which population monotonicity (no player is worse off when additional players enter the game) and egalitarian core selection (no other core allocation can be obtained by a single transfer from a richer to a poorer player) are compatible, which is the class of games ...

Added: February 25, 2026

Assessing transfer functions in control systems

Gribkova N., Zitikis R., Journal of Statistical Theory and Practice 2019 Vol. 13 No. 1 P. 1–33

When dealing with control systems, it is useful and even necessary to assess the performance of underlying transfer functions. The functions may or may not be linear, may or may not be monotonic. They may have structural breaks and other aberrations that require monitoring and quantification to aid decision making. The present paper develops such ...

Added: February 28, 2020

Monotone Conformance Checking for Partially Matching Designed and Observed Processes

Polyvyanyy A., Kalenkova A. A., , in: 2019 International Conference on Process Mining (ICPM).: IEEE, 2019. P. 81–88.

Conformance checking is a subarea of process mining that studies relations between designed processes, also called process models, and records of observed processes, also called event logs. In the last decade, research in conformance checking has proposed a plethora of techniques for characterizing the discrepancies between process models and event logs. Often, these techniques are ...

Added: October 13, 2019

Полуполе с обобщенным сложением: основные свойства и некоторые приложения в экономике

Matveenko V., В кн.: Модели и методы тропической математики в прикладных задачах экономики и управленияВып. 2.: СПб.: ВВМ, 2014. Гл. 1 С. 4–23.

Рассматриваются различные варианты CES-функций, получившие распространение в экономике. С точки зрения тропической математики CES-функция без весов интересна тем, что при изменении параметра, связывает идемпотентные операции max и min со стандартной динейно-алгебраической операцией +. Мы рассматриваем CES-функции с позиций тропической математики на основе введения операции обобщенного сложения. Исследуются свойства монотонности, взаимосвязь различных видов CES-функции, а также ...

Added: December 29, 2014

The nucleolus and the tau-value of interval games

Yanovskaya E. B., , in: Contributions to game theory and managementIssue 3.: St. Petersburg: Graduate School of Management, St. Petersburg University, 2010. P. 421–430.

Interval cooperative games are models of cooperative situation where only bounds for payoffs of coalitions are known with certainty. The extension of solutions of classical cooperative games to interval setting highly depends on their monotonicity properties. However. both the prenucleolus and the tau-value are not aggregate monotonic on the class of convex TU games Hokari ...

Added: March 20, 2014

Collective decision making

Dordrecht: Springer, 2010.

Added: March 20, 2014

Cовместная аксиоматизция пред n-ядра и решения Дутты-Рэя для выпуклых игр

Yanovskaya E. B., Математическая теория игр и ее приложения 2012 Т. 4 № 2 С. 96–123

Most of solutions for cooperative games with transferable utilities (TU) are covariant with respect to positive linear transformations of individual utilities. However, this property does not take into account interpersonal comparisons of players' payoffs. The constrained egalitarian solution defined by Dutta and Ray for the class of convex TU games, being not covariant, served as ...

Added: March 20, 2014