Synergy brittleness in decentralized minimax decision problems

When a subset of agents achieves the optimal cost of the full system synergy is brittle. A finite horizon, decentralized, minimax decision problem is considered, necessary and sufficient conditions for synergy brittleness are derived. It is shown that synergy brittleness results in decoupled subsystems. The decoupling is used to derive necessary and sufficient conditions for a decomposition of the optimization problem. A distributed cliquing algorithm that efficiently computes the decomposition is given, and uniformly optimal policies for each subproblem are derived. The methods developed herein are applicable to the optimization of large, multiagent systems. The results are illustrated on a perimeter patrolling example.