Synthesis of Deceptive Strategies in Reachability Games with Action Misperception

We consider a class of two-player turn-based zero-sum games on graphs with reachability objectives, known as reachability games, where the objective of Player 1 (P1) is to reach a set of goal states, and that of Player 2 (P2) is to prevent this. In particular, we consider the case where the players have asymmetric information about each other's action capabilities: P2 starts with an incomplete information (misperception) about P1's action set, and updates the misperception when P1 uses an action previously unknown to P2. When P1 is made aware of P2's misperception, the key question is whether P1 can control P2's perception so as to deceive P2 into selecting actions to P1's advantage? We show that there might exist a deceptive winning strategy for P1 that ensures P1's objective is achieved with probability one from a state otherwise losing for P1, had the information being symmetric and complete. We present three key results: First, we introduce a dynamic hypergame model to capture the reachability game with evolving misperception of P2. Second, we present a fixed-point algorithm to compute the Deceptive Almost-Sure Winning (DASW) region and DASW strategy. Finally, we show that DASW strategy is at least as powerful as Almost-Sure Winning (ASW) strategy in the game in which P1 does not account for P2's misperception. We illustrate our algorithm using a robot motion planning in an adversarial environment.