Optimism pessimism stability in the graph model for conflict resolution for multilateral conflicts.

In this article, we introduce a new solution concept for the graph model for conflict resolution (GMCR) for situations where decision makers (DMs) have no information about their opponents' preferences or act not using this information. Many classical stability concepts used in the GMCR are based on a con-servative attitude of DMs. Here we propose to incorporate a degree of optimism to allow for more types of attitudes under uncertainty. More specifically, inspired by the notions of Lh stability and Maximinh stability, we present the Optimism Pessimism stability for conflicts involving any finite number of DMs considering that a DM anticipates his/her own benefits looking an arbitrary number of rounds ahead, called horizon and denoted by h , and uses his/her degree of optimism to evaluate his/her anticipated payoff according to the worst and best scenarios that can be achieved. We investigate how the degree of optimism and the conflict horizon influence the stability of states. We also analyse how the optimism pessimism stability is related to other stabilities commonly used in GMCR. Finally, this new solution con-cept is applied to the multilateral dispute over water export from Lake Gisborne.(c) 2023 Elsevier B.V. All rights reserved.