  Deception is helpful for agents masking their intentions from an observer. We
consider a team of agents deceiving their supervisor. The supervisor defines
nominal behavior for the agents through reference policies, but the agents
share an alternate task that they can only achieve by deviating from these
references. Consequently, the agents use deceptive policies to complete the
task while ensuring that their behaviors remain plausible to the supervisor. We
propose a setting with centralized deceptive policy synthesis and decentralized
execution. We model each agent with a Markov decision process and constrain the
agents' deceptive policies so that, with high probability, at least one agent
achieves the task. We then provide an algorithm to synthesize deceptive
policies that ensure the deviations of all agents are small by minimizing the
worst Kullback-Leibler divergence between any agent's deceptive and reference
policies. Thanks to decentralization, this algorithm scales linearly with the
number of agents and also facilitates the efficient synthesis of reference
policies. We then explore a more general version of the deceptive policy
synthesis problem. In particular, we consider a supervisor who selects a subset
of agents to eliminate based on the agents' behaviors. We give algorithms to
synthesize deceptive policies such that, after the supervisor eliminates some
agents, the remaining agents complete the task with high probability. We also
demonstrate the developed methods in a package delivery example.
