In October 2026 two independent groups claimed deterministic algorithms that count the satisfying assignments of a k-CNF formula in time 2^{o(n)}, refuting the Exponential Time Hypothesis (ETH). We ask what these claims imply for the exact analysis of equilibria in games where each player interacts with a bounded number of others. Conditional on the claimed … Read more
Multi-leader-follower games arise when modeling competition between two or more dominant firms and lead in a natural way to equilibrium problems with equilibrium constraints (EPECs). We examine a variety of nonlinear optimization and nonlinear complementarity formulations of EPECs. We distinguish two broad cases: problems where the leaders can cost-differentiate and problems with price-consistent followers. We … Read more
We consider the problem of maximizing the revenue raised from tolls set on the arcs of a transportation network, under the constraint that users are assigned to toll-compatible shortest paths. We first prove that this problem is strongly NP-hard. We then provide a polynomial time algorithm with a worst-case precision guarantee of $\frac{1}{2}\log m_T+1$, where … Read more