Deterministic quasipolynomial-time mean-payoff games

We give a deterministic algorithm that computes the complete zero-threshold winning set of a finite mean-payoff game with arbitrary signed integer edge weights encoded in binary. For total explicit input length L, it uses $2^{O((\log (L+2){)}^2)}$ bit operations. A reduction also computes the exact rational value at every vertex and globally optimal positional strategies for both players within the same quasipolynomial bound.