Dynamic network analysis of a target defense differential game with limited observations

TL;DR

This paper models a multi-player differential game involving a target, attacker, and defenders with limited observation capabilities, introducing network-based strategies and equilibrium analysis to optimize their interactions.

Contribution

It develops a novel framework for dynamic target defense games with asymmetric and limited observations, using network-adapted feedback strategies and inverse game theory.

Findings

Derived network-adapted feedback Nash strategies

Introduced a consistency criterion for strategy refinement

Validated strategies through numerical experiments

Abstract

In this paper, we study a Target-Attacker-Defender (TAD) differential game involving one attacker, one target and multiple defenders. We consider two variations where (a) the attacker and the target have unlimited observation range and the defenders are visibility constrained (b) only the attacker has unlimited observation range and the remaining players are visibility constrained. We model the players' interactions as a dynamic game with asymmetric information. Here, the visibility constraints of the players induce a visibility network which encapsulates the visibility information during the evolution of the game. Based on this observation, we introduce network adapted feedback or implementable strategies for visibility constrained players. Using inverse game theory approach we obtain network adapted feedback Nash equilibrium strategies. We introduce a consistency criterion for selecting a subset (or refinement) of network adapted feedback Nash strategies, and provide an optimization based approach for computing them. Finally, we illustrate our results with numerical experiments.