Introducing Credible Movements in the Optimism Pessimism Stability in the Graph Model

The behaviour of decision makers (DMs) is an important aspect in the analysis of strategic conflicts. The Graph Model for Conflict Resolution (GMCR) is a systematic methodology that enables to simulate DMs interactions in conflict situations by using several stability definitions capable of capturing features of human behaviour, pointing out recommendations for the decision making process. However, not every DM behaviour can be captured by the existing GMCR solution concepts, so that the proposal of new ones is justified. In this sense, the objective of this work is to extend the Optimism Pessimism Stability by requiring that some or all DMs only make credible moves. In Credible Optimism Pessimism Stabilities (COPS), DMs average over the best and worst case scenarios according to a degree of optimism (DGO), however, a DM only leaves a state when the next one is preferable for him or her. Thus, DMs do not accept the risk to reach a lower payoff in the short term, anticipating to receive a better payoff in the long term. Following, the study investigates the consequences of changing the DGO and the conflict horizon in the states’ stability. Relations among the new stability definitions and other GMCR stability concepts are also analysed. An application to the Lake Gisborne conflict illustrates how the requirement of credible moves can alter the degree of optimism necessary for states’ stability.