Quasi-Equilibrium Pairs in Pursuit Games on a Cyclic Graph: Some Modified Cases

In this paper, three special pursuit games on cyclic graphs are solved. These games are relevant to unsolved problems initiated by a game without a value. The following problems are proposed i For a finite or infinite game without a saddle point, how should the players make their decisions Here, we suppose that the game is played once. Thus mixed strategies are not considered. ii For an infinite game without a value v, i.e., V1v2, how should the players make their decisions To answer these questions, new concepts of quasi-equilibrium and pseudo-equilibrium are defined and it is shown that a game MDCPG has a quasi-equilibrium pair. Keywords Pursuit games, Geometric games Cyclic graphs Quasi-equilibrium, Pseudo-equilibrium.