Quantitative Planning with Action Deception in Concurrent Stochastic Games

We study a class of two-player competitive concurrent stochastic games on graphs with reachability objectives. Specifically, player 1 aims to reach a subset $F_1$ of game states, and player 2 aims to reach a subset $F_2$ of game states where $F_2\cap F_1=\emptyset$. Both players aim to satisfy their reachability objectives before their opponent does. Yet, the information players have about the game dynamics is asymmetric: P1 has a (set of) hidden actions unknown to P2 at the beginning of their interaction. In this setup, we investigate P1's strategic planning of action deception that decides when to deviate from the Nash equilibrium in P2's game model and employ a hidden action, so that P1 can maximize the value of action deception, which is the additional payoff compared to P1's payoff in the game where P2 has complete information. Anticipating that P2 may detect his misperception about the game and adapt his strategy during interaction in unpredictable ways, we construct a planning problem for P1 to augment the game model with an incomplete model about the theory of mind of the opponent P2. While planning in the augmented game, P1 can effectively influence P2's perception so as to entice P2 to take actions that benefit P1. We prove that the proposed deceptive planning algorithm maximizes a lower bound on the value of action deception and demonstrate the effectiveness of our deceptive planning algorithm using a robot motion planning problem inspired by soccer games.