In strategic conflicts, the behavior of decision makers (DMs) is affected by their beliefs about how their opponents will respond, how they will counter respond, and more generally by the number of action-reaction steps they consider. In this article, we propose several notions of stability with variable horizon that vary in whether the focal DM and her opponents are allowed to make moves that are immediately disadvantageous, called unilateral disimprovements. Credible maximin stability reflects the assumption that opponents will attempt to deter a focal DM from a move by imposing the strongest possible sanction. We analyze the effects of varying the horizon on this form of stability, and on the relationships among the solution concepts that result. Requiring the focal DM to make only unilateral improvements does not influence the stability of states, but restricting opponents’ responses to unilateral improvements reduces the set of stable states. An application to a water-pricing conflict illustrates the analysis of a graph model using credible maximin stabilities.

In this paper, we modify the graph model for conflict resolution (GMCR) to model interactive unawareness of decision makers (DMs) about the options available to them in the conflict. More specifically, we consider a GMCR with two DMs, where a DM, in some given state, can be unconscious about some of his options, or about the options of his opponent, and therefore, may have only a partial knowledge of the state space. By interactive unawareness, it is meant that a DM can reason about the awareness level of the other DM and about the awareness level of the other DM regarding his or her own awareness level and so on. We generalize standard solution concepts for this model and illustrate its usefulness by means of a hypothetical war conflict.

We present three problems found in this paper “Policy equilibrium and generalized metarationalities for multiple decision-maker conflicts,” by Zeng et al., published in IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 37, no. 4, pp. 456-463, Jul. 2007. More specifically, we show by means of counterexamples that: 1) the definition proposed for n-decision maker (DM) conflicts does not coincide with the existing generalized metarationality defined by these same authors for conflicts with 2 DMs; 2) the equivalence between generalized metarationality for 2 rounds and symmetric metarational stability is false; and 3) generalized metarational equilibrium does not imply policy equilibrium.

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 Maximinhstability with horizon h for a given DM. The Maximinhstability concept was inspired by the notion of limited-move stability with horizon h 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 Maximinhstabilities for different horizons and the relationship among Maximinhstability and other GMCR stability concepts. Finally, we present an application to illustrate the proposed stability concept, namely, a neuroscience technological selection conflict in China.