Theory of satisfactory decisions and its application to conflict resolution

In most conflict situations, when the interests and preferences of agents diverge, optimal decision theory in applied. This involves for each agent to make decisions that maximize his or her own expected utility. In most complex cases, when the decision of an agent depends on the decision of another agent, game theory is applied, reaching Nash equilibrium. However, one can show that, under this paradigm, the absolute gain for an agent that optimizes his decision may be very small, albeit it is superior to the gain of his opponent. We propose another approach, namely the satisfactory decision theory. A satisfactory decision for a group of agents can lead to better profits for the whole group, although the gain of each agent is not optimal. Moreover, each agent´s satisfactory decision is compatible with the satisfactory decision of the group. A description of the situation is given in terms of graphs and probabilities. The individual preferences and the inclination to tradeoff are quantitatively defined for each agent. The method provides conditions for satisfactory decisions to be made. We apply the method to the case when competitive agents are bound to cooperate.