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

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.Comment: 8 figure

Desensitization and Deception in Differential Games with Asymmetric Information

Desensitization addresses safe optimal planning under parametric uncertainties by providing sensitivity function-based risk measures. This paper expands upon the existing work on desensitization to address safe planning for a class of two-player differential games. In the proposed game, parametric uncertainties correspond to variations in a vector of model parameters about its nominal value. The two players in the proposed formulation are assumed to have information about the nominal value of the parameter vector. However, only one of the players is assumed to have complete knowledge of parametric variation, creating a form of information asymmetry in the proposed game. The lack of knowledge regarding the parametric variations is expected to result in state constraint violations for the player with an information disadvantage. In this regard, a desensitized feedback strategy that provides safe trajectories is proposed for the player with incomplete information. The proposed feedback strategy is evaluated in instances involving one pursuer and one evader with an uncertain dynamic obstacle, where the pursuer is assumed to know only the nominal value of the obstacle's speed. At the same time, the evader knows the obstacle's true speed, and also the fact that the pursuer possesses only the nominal value. Subsequently, deceptive strategies are proposed for the evader, who has an information advantage, and these strategies are assessed against the pursuer's desensitized strategy

Efficient Communication for Pursuit-Evasion Games with Asymmetric Information

We consider a class of pursuit-evasion differential games in which the evader has continuous access to the pursuer's location, but not vice-versa. There is an immobile sensor (e.g., a ground radar station) that can sense the evader's location and communicate that information intermittently to the pursuer. Transmitting the information from the sensor to the pursuer is costly and only a finite number of transmissions can happen throughout the entire game. The outcome of the game is determined by the control strategies of the players and the communication strategy between the sensor and the pursuer. We obtain the (Nash) equilibrium control strategies for both the players as well as the optimal communication strategy between the static sensor and the pursuer. We discuss a dilemma for the evader that emerges in this game. We also discuss the emergence of implicit communication where the absence of communication from the sensor can also convey some actionable information to the pursuer

Optimal Intermittent Sensing for Pursuit-Evasion Games

We consider a class of pursuit-evasion differential games in which the evader has continuous access to the pursuer's location, but not vice-versa. There is a remote sensor (e.g., a radar station) that can sense the evader's location upon a request from the pursuer and communicate that sensed location to the pursuer. The pursuer has a budget on the total number of sensing requests. The outcome of the game is determined by the sensing and motion strategies of the players. We obtain an equilibrium sensing strategy for the pursuer and an equilibrium motion strategy for the evader. We quantify the degradation in the pursuer's pay-off due to its sensing limitations

An All-Against-One Game Approach for the Multi-Player Pursuit-Evasion Problem

The traditional pursuit-evasion game considers a situation where one pursuer tries to capture an evader, while the evader is trying to escape. A more general formulation of this problem is to consider multiple pursuers trying to capture one evader. This general multi-pursuer one-evader problem can also be used to model a system of systems in which one of the subsystems decides to dissent (evade) from the others while the others (the pursuer subsystems) try to pursue a strategy to prevent it from doing so. An important challenge in analyzing these types of problems is to develop strategies for the pursuers along with the advantages and disadvantages of each. In this thesis, we investigate three possible and conceptually different strategies for pursuers: (1) act non-cooperatively as independent pursuers, (2) act cooperatively as a unified team of pursuers, and (3) act individually as greedy pursuers. The evader, on the other hand, will consider strategies against all possible strategies by the pursuers. We assume complete uncertainty in the game i.e. no player knows which strategies the other players are implementing and none of them has information about any of the parameters in the objective functions of the other players. To treat the three pursuers strategies under one general framework, an all-against-one linear quadratic dynamic game is considered and the corresponding closed-loop Nash solution is discussed. Additionally, different necessary and sufficient conditions regarding the stability of the system, and existence and definiteness of the closed-loop Nash strategies under different strategy assumptions are derived. We deal with the uncertainties in the strategies by first developing the Nash strategies for each of the resulting games for all possible options available to both sides. Then we deal with the parameter uncertainties by performing a Monte Carlo analysis to determine probabilities of capture for the pursuers (or escape for the evader) for each resulting game. Results of the Monte Carlo simulation show that in general, pursuers do not always benefit from cooperating as a team and that acting as non-cooperating players may yield a higher probability of capturing of the evader