Several axiomatizations of the class \(\text{RCA}_{\alpha}\) exist in the literature, but none has been known for \(\text{RQPEA}_{\alpha}\) when \(\alpha \geq 3\). Here, using games, as introduced by Hirsch and Hodkinson in algebraic logic, a recursive axiomatization of the class \(\text{ RQPEA}_{\alpha}\) of representable quasi-polyadic equality algebras of any dimension \(\alpha\) is given. Following Sain and Thompson in modifying Andréka's methods of splitting, to adapt the quasi-polyadic equality case it is shown that if \(\sigma\) is a set of equations axiomatizing \(\text{RPEA}_{n}\) for \(2