Minimax regret stability in the graph model for conflict resolution

Abstract

In strategic conflicts, decision-makers (DMs) do not constantly make their best decisions, which makes room for DMs to feel regretful. In this context, this work proposes the Minimax Regret Stability within the graph model for conflict resolution (GMCR) for modelling and analysing conflicts, considering that DMs would feel regret for an unsatisfactory decision. This concept does not require knowledge about the opponent’s preference in bilateral conflicts. The aim of the new solution concept is to recommend a state as stable if there exists a policy recommending to stay at that state which minimizes the maximum regret of the DM for a given conflict horizon, where a policy specifies what action a DM must choose in every conflict state. In addition, we investigate the relations among the Minimax regret stability and other classical GMCR solution concepts. Following, the influence of the horizon on the stability of states is also studied. Finally, a truckers’ strike conflict was used to illustrate how the new solution concept can provide valuable strategic insights in real-life conflict situations.