  Making decisions in the presence of a strategic opponent requires one to take
into account the opponent's ability to actively mask its intended objective. To
describe such strategic situations, we introduce the non-cooperative inverse
reinforcement learning (N-CIRL) formalism. The N-CIRL formalism consists of two
agents with completely misaligned objectives, where only one of the agents
knows the true objective function. Formally, we model the N-CIRL formalism as a
zero-sum Markov game with one-sided incomplete information. Through interacting
with the more informed player, the less informed player attempts to both infer,
and act according to, the true objective function. As a result of the one-sided
incomplete information, the multi-stage game can be decomposed into a sequence
of single-stage games expressed by a recursive formula. Solving this recursive
formula yields the value of the N-CIRL game and the more informed player's
equilibrium strategy. Another recursive formula, constructed by forming an
auxiliary game, termed the dual game, yields the less informed player's
strategy. Building upon these two recursive formulas, we develop a
computationally tractable algorithm to approximately solve for the equilibrium
strategies. Finally, we demonstrate the benefits of our N-CIRL formalism over
the existing multi-agent IRL formalism via extensive numerical simulation in a
novel cyber security setting.
