On the symmetry relation between different characteristic functions for additively separable cooperative games

Ekaterina Gromova; Kirill Savin

doi:10.3934/jdg.2022017

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2023, Volume 10, Issue 1: 1-10. Doi: 10.3934/jdg.2022017

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On the symmetry relation between different characteristic functions for additively separable cooperative games

Ekaterina Gromova^1, , and
Kirill Savin^2,

1.
Department of Mathematics, Higher School of Economics St. Petersburg Campus, St. Petersburg Russia
2.
Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, St. Petersburg Russia

^*Corresponding author: Ekaterina Gromova, e-mail: ekaterina.shevkoplyas@gmail.com
^*Corresponding author: Ekaterina Gromova, e-mail: ekaterina.shevkoplyas@gmail.com

Received: January 2022

Revised: March 2022

Early access: July 2022

Published: January 2023

This study was partially done while E. Gromova was with St. Petersburg State University

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Abstract

We analyze 4 characteristic functions $ V^\alpha $, $ V^\delta $, $ V^\zeta $, and $ V^\eta $, and give a necessary condition for these functions to satisfy the relation $ V^\alpha - V^\delta = V^\zeta - V^\eta $ for all coalitions $ S $. To do so, we define and formally analyze the class of additively separable games. It is shown that many important types of games, both static and dynamic, belong to this class.

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Mathematics Subject Classification: Primary: 91A12;Secondary: 91A06.

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References

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