The replicator dynamics of zero-sum games arise from a novel poisson algebra

We show that the replicator dynamics for zero-sum games arises as a result of non-canonical bracket is hybrid between Poisson Bracket and Nambu Bracket. The resulting parameterized both by skew-symmetric payoff matrix mediating function. function only sometimes conserved quantity, but plays critical role in determination dynamics. As by-product, we this definition natural metric on which phase flow-volume preserved. Additionally, satisfies all same identities except Jacobi identity (JI), satisfied special cases In particular, gives rise to yields JI. This neatly explains why allows us derive flow suggests geometry extends Symplectic potentially an alternate approach quantizing evolutionary games.