Tatiana N. Fomenko
Applications of Fixed Point Theorems to the Problem of the Equilibrium Strategy Existence Preservation in a Parametric Family of Antagonistic Games
Dynamic Systems and Applications .32 (2023) 55-67

https://doi.org/10.46719/dsa2023.32.04

ABSTRACT.
For a parametric family of antagonistic games with two players, the problem is considered of the equilibrium strategy existence preservation, under the changing of the parameter. This issues are considered both in the case when the players’ strategy spaces are ordered sets, and in the case of metric players’ strategy spaces. Some previous results are used concerning fixed point existence preservation in metric spaces, as well as similar results in ordered sets.

AMS (MOS) Subject Classification. 47H10, 54H25, 49M25, 06A06, 91A05, 91A11.

Key Words and Phrases. orderly covering mapping, isotone mapping, $(\alpha,\beta)$-search functional, cascade search principle, parametric antagonistic game, multivalued mapping, fixed point, coincidence point.