Abstract: Differential games are a class of game theory problems governed by differential equations. Differential games are often defined in the continuous domain and solved by the calculus of variations. However, modelling and solving these games are not straightforward tasks. Differential games, like game theory, are often involved with social dilemmas and social behaviours. Modelling these social phenomena with mathematical tools is often problematic. In this paper, we modelled deception to increase the pay-off in differential games. Deception is modelled as a bi-level policy system, and each level is modelled with a fuzzy controller. Fuzzy controllers are trained using a novel hierarchical fuzzy actor-critic learning algorithm. A deceitful player plays against multiple opponents. Although there is one ultimate goal for the player, it can choose multiple fake goals as well. The intention is to find a strategy to switch between the fake goals and the true goal to fool the opponents. The simulation platform is the game of guarding territories, a specific form of the pursuit-evasion games. We propose a method to easily increase the number of defenders with minimum changes in the policies. We create a universal structure that is not affected by the curse of dimensionality. We show that a discerning invader capable of using deception can improve its performance against the defenders by increasing the chance of invasion. We investigate the single-invader single-defender game and the single-invader multi-defender game. We study the superior invader and agents with the same speed. In all mentioned situations, the invader increases its pay-off by using deception versus being honest. A two-level policy system is used in this paper to model deception. The lower-level policy controls each goal's invasion actions, while the higher-level policy controls deception where a successful game is not initially possible. PDF
Keywords: Differential Games, Reinforcement Learning, Actor-Critic Learning, Fuzzy Systems