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Open AccessArticle

The Relationship between the Core and the Modified Cores of a Dynamic Game

by Artem Sedakov 1,2,3,* and Hao Sun 1
1
Saint Petersburg State University, 7/9 Universitetskaya nab., 199034 Saint Petersburg, Russia
2
School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
3
Institute of Applied Mathematics of Shandong, Qingdao 266071, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(6), 1023; https://doi.org/10.3390/math8061023
Received: 21 May 2020 / Revised: 20 June 2020 / Accepted: 22 June 2020 / Published: 23 June 2020
(This article belongs to the Special Issue Game Theory)
The core as a solution to a cooperative game has the advantage that any imputation from it is undominated. In cooperative dynamic games, there is a known transformation that demonstrates another advantage of the core—time consistency—keeping players adhering to it during the course of the game. Such a transformation may change the solution, so it is essential that the new core share common imputations with the original one. In this paper, we will establish the relationship between the original core of a dynamic game and the core after the transformation, and demonstrate that the latter can be a subset of the former. View Full-Text
Keywords: discrete-time games; cooperation; the core; linear transformation discrete-time games; cooperation; the core; linear transformation
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Sedakov, A.; Sun, H. The Relationship between the Core and the Modified Cores of a Dynamic Game. Mathematics 2020, 8, 1023.

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