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Towards a formal framework for multi-objective multiagent planning

Multi-Objective Multiagent Planning (MOMAP) addresses the problem of resolving conflicts between individual agent interests and the group interests. In this paper, we address this problem by presenting a formal framework to represent objective relationships, a decision model using a Vector-Valued Decentralized Markov Decision Process (2V-DEC-MDP) and an algorithm to solve the resulting 2V-DEC-MDP. The formal framework of a Vector-Valued MDP considered uses the value function which returns a vector representing the individual and the group interests. An optimal policy in such contexts is not clear but in this approach we develop a regret-based technique to find a good tradeoff between the group and individual interests. To do that, the approach we present uses Egalitarian Social Welfare orderings that allow an agent to consider during its local optimization the satisfaction of all criteria and reducing their differences. The obtained result is a good balance between individual and group satisfactions where the local policies can lead to more global satisfying behaviors in some settings. This result is illustrated in many examples and compared to alternate local policies.