Fair parity/parity games with fairness constraints on both players are solvable via a polynomial gadget reduction to ordinary parity games or a direct symbolic fixpoint algorithm.
Handbook of Formal Language The- ory III, 389–455 (1997)
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Doubly Fair Parity Games
Fair parity/parity games with fairness constraints on both players are solvable via a polynomial gadget reduction to ordinary parity games or a direct symbolic fixpoint algorithm.