Risk-Sharing Mechanism Design in Non-Cooperative Multi-Defender Stackelberg Defense Resources Allocation Game

Government bodies, companies, and social agencies typically act as defenders and apply the game theory method to protect their assets targeted by malicious attackers. However, for developed transregional or even transnational systems, the upper-level administrator fails to coordinate the lower-level agents (sub-system defenders) due to the organizational and beneficial boundaries. This work focuses on the anarchy phenomenon of such decentralized non-cooperative multiagent systems, and proposes a non-cooperative multi-defender Stackelberg defense resources allocation game model to analyze the attack defense confrontation process. We also discuss homogeneous systems analytically and explore general systems numerically to reveal the relationships between the anarchy phenomenon and system parameters, which extends the generality of such problems and provides the upper-level administrator with useful information on constructing a decentralized multiagent system. Besides, to mitigate the anarchy phenomenon, this work first designs a risk-sharing mechanism to support the upper-level administrator in coordinating non-cooperative defenders from an individual-optimal defense strategy to a global-optimal one. The proposed risk-sharing mechanism is established, and the anarchy phenomenon is analyzed to the target system managed by multiple non-cooperative defenders. Simulations on the local metering system also show small investment in the risk-sharing mechanism could reduce considerable total social welfare loss.
Note to Practitioners
—This paper is motivated by the practical demand of protecting decentralized non-cooperative multiagent systems consisting of several beneficial-independent agents (sub-system defenders) and one weak administrator, such as cross-region power grids, and cross-region water distribution systems. Different from previous works allocating resources global-optimally, this study focuses on excessive or insufficient resources allocation due to the anarchy phenomenon. We then design a risk-sharing mechanism for the administrator of the decentralized non-cooperative multiagent system. Based on this, subsystem system operators would follow the instruction from the system-level administrator instead of implementing a local-optimal defense strategy. The proposed model and method are demonstrated by numerical experiments on the local metering system, and can be applied to many decentralized multiagent systems. For example, non-cooperative power companies would follow the instruction on global-optimal defense resources allocation on smart meters from the upper-level administrator.