On some properties of limited move stability, generalized metarationality, and policy equilibrium in bilateral conflicts

In the Graph Model for Conflict Resolution (GMCR), conflicts are analyzed as in a chess game foreseeing a sequence of moves and countermoves, where the length of this sequence is known as the conflict horizon. In the literature, the stability concepts mostly used are with a fixed horizon, but there are concepts that accommodate a variable horizon. Although these latter concepts have a higher flexibility, they are not applied very frequently perhaps because their properties are not so well understood. In this article, our objective is to shed some light in three stability concepts with variable horizon: limited move, generalized metarationality stabilities and policy equilibrium in bilateral conflicts. In particular, we present some existing inaccuracies in the literature of the GMCR, regarding these concepts. First, we observed that the state anticipated by the focal decision maker (DM) in the limited move stability is not necessarily unique when both the focal DM and his/her opponent move seeking to maximize their respective gains and the focal DM knows his/her opponent’s preferences. Next, we present a counterexample to a result in the literature that relates generalized metarationalities and policy equilibria. Finally, we present a formal proof that Lh implies the MRh stability, and show that the existing justification for this result in the GMCR literature has a problem.