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We motivate and propose a new model for non-cooperative Markov game whichconsiders the interactions of risk-aware players. This model characterizes thetime-consistent dynamic "risk" from both stochastic state transitions (inherentto the game) and randomized mixed strategies (due to all other players). Anappropriate risk-aware equilibrium concept is proposed and the existence ofsuch equilibria is demonstrated in stationary strategies by an application ofKakutani's fixed point theorem. We further propose a simulation-basedQ-learning type algorithm for risk-aware equilibrium computation. Thisalgorithm works with a special form of minimax risk measures which cannaturally be written as saddle-point stochastic optimization problems, andcovers many widely investigated risk measures. Finally, the almost sureconvergence of this simulation-based algorithm to an equilibrium isdemonstrated under some mild conditions. Our numerical experiments on a twoplayer queuing game validate the properties of our model and algorithm, anddemonstrate their worth and applicability in real life competitivedecision-making.

Model and Reinforcement Learning for Markov Games with Risk Preferences