  Satisfiability checking for monotone modal logic is known to be (only)
NP-complete. We show that this remains true when the logic is extended with
aconjunctive and alternation-free fixpoint operators as well as the universal
modality; the resulting logic -- the aconjunctive alternation-free monotone
$\mu$-calculus with the universal modality -- contains both concurrent
propositional dynamic logic (CPDL) and the alternation-free fragment of game
logic as fragments. We obtain our result from a characterization of
satisfiability by means of B\"uchi games with polynomially many Eloise nodes.
