Synthesis of Deceptive Strategies in Reachability Games with Action Misperception (Technical Report)

Abstract

Strategic deception is an act of manipulating the opponent's perception to gain strategic advantages. In this paper, we study synthesis of deceptive winning strategies in two-player turn-based zero-sum reachability games on graphs with one-sided incomplete information of action sets. In particular, we consider the class of games in which Player 1 (P1) starts with a non-empty set of private actions, which she may 'reveal' to Player 2 (P2) during the course of the game. P2 is equipped with an inference mechanism using which he updates his perception of P1's action set whenever a new action is revealed. Under this information structure, the objective of P1 is to reach a set of goal states in the game graph while that of P2 is to prevent it. We address the question: how can P1 leverage her information advantages to deceive P2 into choosing actions that in turn benefit P1? To this end, we introduce a dynamic hypergame model to capture the reachability game with evolving misperception of P2. Analyzing the game qualitatively, we design algorithms to synthesize deceptive sure and almost-sure winning regions, and establish two key results: (1) under sure-winning condition, deceptive winning strategy is equivalent to the non-deceptive winning strategy - i.e. use of deception has no advantages, (2) under almost-sure winning condition, the deceptive winning strategy could be more powerful than the non-deceptive strategy. We illustrate our algorithms using a capture-the-flag game, and demonstrate the use of proposed approach to a larger class of games with temporal logic objectives.