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Classical game-theoretic approaches for multi-agent systems in both theforward policy design problem and the inverse reward learning problem oftenmake strong rationality assumptions: agents perfectly maximize expectedutilities under uncertainties. Such assumptions, however, substantiallymismatch with observed humans' behaviors such as satisficing with sub-optimal,risk-seeking, and loss-aversion decisions. In this paper, we investigate theproblem of bounded risk-sensitive Markov Game (BRSMG) and its inverse rewardlearning problem for modeling human realistic behaviors and learning humanbehavioral models. Drawing on iterative reasoning models and cumulativeprospect theory, we embrace that humans have bounded intelligence and maximizerisk-sensitive utilities in BRSMGs. Convergence analysis for both the forwardpolicy design and the inverse reward learning problems are established underthe BRSMG framework. We validate the proposed forward policy design and inversereward learning algorithms in a navigation scenario. The results show that thebehaviors of agents demonstrate both risk-averse and risk-seekingcharacteristics. Moreover, in the inverse reward learning task, the proposedbounded risk-sensitive inverse learning algorithm outperforms a baselinerisk-neutral inverse learning algorithm by effectively recovering not only moreaccurate reward values but also the intelligence levels and the risk-measureparameters given demonstrations of agents' interactive behaviors.

Bounded Risk-Sensitive Markov Games: Forward Policy Design and Inverse Reward Learning with Iterative Reasoning and Cumulative Prospect Theory