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Markov games (MGs) and multi-agent reinforcement learning (MARL) are studied to model decision making in multi-agent systems. Traditionally, the objective in MG and MARL has been risk-neutral, i.e., agents are assumed to optimize a performance metric such as expected return, without taking into account subjective or cognitive preferences of themselves or of other agents. However, ignoring such preferences leads to inaccurate models of decision making in many real-world scenarios in finance, operations research, and behavioral economics. Therefore, when these preferences are present, it is necessary to incorporate a suitable measure of risk into the optimization objective of agents, which opens the door to risk-sensitive MG and MARL. In this paper, we systemically review the literature on risk sensitivity in MG and MARL that has been growing in recent years alongside other areas of reinforcement learning and game theory. We define and mathematically describe different risk measures used in MG and MARL and individually for each measure, discuss articles that incorporate it. Finally, we identify recent trends in theoretical and applied works in the field and discuss possible directions of future research., Comment: 14 pages, 2 figures, 1 table

Classical multi-agent reinforcement learning (MARL) assumes risk neutrality and complete objectivity for agents. However, in settings where agents need to consider or model human economic or social preferences, a notion of risk must be incorporated into the RL optimization problem. This will be of greater importance in MARL where other human or non-human agents are involved, possibly with their own risk-sensitive policies. In this work, we consider risk-sensitive and non-cooperative MARL with cumulative prospect theory (CPT), a non-convex risk measure and a generalization of coherent measures of risk. CPT is capable of explaining loss aversion in humans and their tendency to overestimate/underestimate small/large probabilities. We propose a distributed sampling-based actor-critic (AC) algorithm with CPT risk for network aggregative Markov games (NAMGs), which we call Distributed Nested CPT-AC. Under a set of assumptions, we prove the convergence of the algorithm to a subjective notion of Markov perfect Nash equilibrium in NAMGs. The experimental results show that subjective CPT policies obtained by our algorithm can be different from the risk-neutral ones, and agents with a higher loss aversion are more inclined to socially isolate themselves in an NAMG.