We propose and address a new variation of the team orienteering problem (TOP) in which all members of the team are independent self-interested agents. The prize-collecting nature emanates from the fact that the prize available at a node of the traversal graph can be collected only by a single visiting agent. The problem is motivated by situations in which team members (agents) must accomplish tasks toward a common goal but are unable to communicate, such as a fleet of surveillance drones operating in a communication denied area or with remote pilots operating independently. We explore three policies for minimizing the amount of inefficiency these self-interested agents can bring into the situation. We analyze these policies in a game-theoretic framework and show upper bounds on the Price of Anarchy (PoA) ranging from $\approx 1.582$ to unbounded depending on the policy, network type, and the number of players $k$ . This is done by extending well-known PoA bounds for valid utility systems to a leader–follower setting. The PoA also depends on the behavior of the agents, which could not have goodwill toward other agents. In many cases, we are able to provide examples that establish the tightness of the bounds. Finally, solution methods are provided for each of these policies. Numerical results computed by these solution methods are then presented and compared with the optimal centrally coordinated solutions. Note to Practitioners—Unmanned aerial vehicles (UAVs) are becoming increasingly popular for information collection tasks in defense and civilian applications alike. When the collection area is large, it is not unusual that a fleet of UAVs is deployed. Routing of a fleet can be performed in a centralized or decentralized manner. Decentralized routing might be the only possibility when centralized situational awareness is not possible due to bandwidth limitations and when centralized optimal routes for each UAV are too complex to compute. For managers of UAV syste...