Multiplayer Pursuit-Evasion Differential Games with Uncertain Perceptions: A Cumulative Prospect Theory Approach

This paper establishes, for the first time, a Cumulative Prospect Theory (CPT)-based multiplayer pursuit-evasion (MPE) differential game framework to capture the subjective irrationality of pursuers and evaders in perceiving adversaries’ policies. In the case of deterministic perceptions, a Nash policy can be designed through the MPE differential game formulation. When policy iterations follow a probability distribution, CPT is incorporated into the conventional MPE differential game to model human prospects under risk preference and probability sensitivity. Subsequently, a perceived Nash policy can be designed, aiming to maximize the prospect function. The effectiveness of the proposed results is demonstrated by a numerical example.