Extend robust zero-sum Markov games to player-specific ambiguity

Extend the optimistic dual robust Bellman framework for online robust zero-sum Markov games to settings with player-specific ambiguity sets, for which the shared-payoff robust minimax analysis does not apply directly.

Background

The paper studies a shared zero-sum payoff in which both the strategic opponent and Nature minimize the same return. It explicitly notes that if each player robustifies a separate subjective payoff, the common Bellman saddle recursion generally fails. Developing a theory for player-specific ambiguity would therefore require handling distinct robustness preferences while preserving meaningful equilibrium and regret guarantees.