Prospect Theoretic Approach to Pursuit-evasion Differential Games with Risk Aversion and Probability Sensitivity

TL;DR

This paper introduces a novel pursuit-evasion differential game model incorporating irrational perceptions like risk aversion and probability sensitivity using Prospect Theory, analyzing equilibria and capturability.

Contribution

It models irrational perceptions within a Bayesian framework, establishes conditions for capturability, and proves the existence of CPT-Nash equilibria, linking behavioral theory with control engineering.

Findings

Irrational behaviors can enhance pursuer or evader success.

Certain captures become possible under irrational perceptions, unlike rational models.

The framework provides a theoretical basis for control in human-machine systems.

Abstract

This paper considers for the first time pursuit-evasion (PE) differential games with irrational perceptions of both pursuer and evader on probabilistic characteristics of environmental uncertainty. Firstly, the irrational perceptions of risk aversion and probability sensitivity are modeled and incorporated within a Bayesian PE differential game framework by using Cumulative Prospect Theory (CPT) approach; Secondly, several sufficient conditions of capturability are established in terms of system dynamics and irrational parameters; Finally, the existence of CPT-Nash equilibria is rigorously analyzed by invoking Brouwer's fixed-point theorem. The new results reveal that irrational behaviors benefit the pursuer in some cases and the evader in others. Certain captures that are unachievable under rational behaviors can be achieved under irrational ones. By bridging irrational behavioral theory with game-theoretic control, this framework establishes a rigorous theoretical foundation for practical control engineering within complex human-machine systems.