Planning in multi-agent environment using strips representation and non-cooperative equilibrium strategy

In multi-agent (multi-robot) environment each agent tries to achieve its own goals leading usually to goals conflict. However, there exists a group of problems with conflicting goals, satisfaction of which is possible simultaneously. Such problems can be modelled as a STRIPS system (for instance Block World environment). If STRIPS planning problem is invertible than it is possible to apply planning under uncertainty methodologies to solve inverted problem and then find a plan that solves multi-agent problem. In the paper, a multi-agent Block World environment is presented as an invertible STRIPS problem. Two cases are considered: when goals conflict and do not conflict. A necessary condition of plan existence is formulated. In the case when goals conflict and agents have different goal preferences we show that it is possible to use non-cooperative equilibrium strategy for modification of the plan found previously. This modification guarantees the best solution (in the sense of non-cooperative equilibrium) for all agents in some cases.