$Maximin_{h}$ Stability in the Graph Model for Conflict Resolution for Bilateral Conflicts

In this paper, our objective is to propose a stability concept within the graph model for conflict resolution (GMCR) that does not require knowledge about preferences of other decision makers (DMs) in the conflict and is flexible to analyze the conflict with variable horizon. For that we propose the use of the maximin decision rule within the GMCR. More specifically, we consider a GMCR with two DMs and introduce the concept of <inline-formula> <tex-math notation="LaTeX">${Maximin}_{h}$ </tex-math></inline-formula> stability with horizon <inline-formula> <tex-math notation="LaTeX">$h$ </tex-math></inline-formula> for a given DM. The <inline-formula> <tex-math notation="LaTeX">${Maximin}_{h}$ </tex-math></inline-formula> stability concept was inspired by the notion of limited-move stability with horizon <inline-formula> <tex-math notation="LaTeX">$h$ </tex-math></inline-formula> present in the GMCR literature and it is adequate for modeling cautious DMs in conflicts where they have no knowledge about the other DM’s preferences. We establish what is the relationship among the <inline-formula> <tex-math notation="LaTeX">${Maximin}_{h}$ </tex-math></inline-formula> stabilities for different horizons and the relationship among <inline-formula> <tex-math notation="LaTeX">${Maximin}_{h}$ </tex-math></inline-formula> stability and other GMCR stability concepts. Finally, we present an application to illustrate the proposed stability concept, namely, a neuroscience technological selection conflict in China.