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Randomized quasipolynomial-time mean-payoff games

OpenAI

OpenAI Mathopenai-math/Randomized-quasipolynomial-time-mean-payoff-gamesSep 25, 2026cs.CCAI-generatedscore 0

We give a randomized 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 on every random tape and is correct with probability at least 7/8. A polynomial-time check certifies the winning regions and positional strategies for both players or reports failure. Independent repetition therefore gives an always-correct algorithm with the same expected quasipolynomial bit bound.

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