  This article studies rational and persistent deception among intelligent
robots to enhance security and operational efficiency. We present an N-player
K-stage game with an asymmetric information structure where each robot's
private information is modeled as a random variable or its type. The deception
is persistent as each robot's private type remains unknown to other robots for
all stages. The deception is rational as robots aim to achieve their deception
goals at minimum cost. Each robot forms a dynamic belief of others' types based
on intrinsic or extrinsic information. Perfect Bayesian Nash equilibrium (PBNE)
is a natural solution concept for dynamic games of incomplete information. Due
to its requirements of sequential rationality and belief consistency, PBNE
provides a reliable prediction of players' actions, beliefs, and expected
cumulative costs over the entire K stages. The contribution of this work is
fourfold. First, we identify the PBNE computation as a nonlinear stochastic
control problem and characterize the structures of players' actions and costs
under PBNE. We further derive a set of extended Riccati equations with
cognitive coupling under the linear-quadratic (LQ) setting and extrinsic belief
dynamics. Second, we develop a receding-horizon algorithm with low temporal and
spatial complexity to compute PBNE under intrinsic belief dynamics. Third, we
investigate a deceptive pursuit-evasion game as a case study and use numerical
experiments to corroborate the results. Finally, we propose metrics, such as
deceivability, reachability, and the price of deception (PoD), to evaluate the
strategy design and the system performance under deception.
