Miltersen's new proof simplifies near-optimal strategies in recursive games

Peter Bro Miltersen's new paper, "Existence and computation of monomial families of near-optimal strategies for recursive games," tackles a core question in game theory: how to compute strategies that are epsilon-optimal for every small epsilon>0. Building on earlier work with Frederiksen, which showed such strategies can be encoded by finitely many monomials (action probabilities as constants times integer powers of epsilon), Miltersen offers a simpler, more constructive proof. The key innovation is replacing semialgebraic selection and Puiseux series with directed-forest polynomials, making the result accessible to a wider audience.

Beyond the elegant proof, Miltersen delivers a deterministic polynomial-time algorithm for rational games with a fixed number N of active states. The algorithm computes the monomial family exactly, returning all algebraic coefficients in a single ordered real univariate representation. Its running time and representation length are bounded by L^{(N+1)^{O(N)}}, where L is the input length. This is a significant step toward practical computation of near-optimal strategies for recursive games, with implications for AI planning, economics, and multi-agent systems.