2023/09/05 by Tom van Dijk, Georg Loho, van Dijk, Tom +3 · 1 citation
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Artificial Intelligence in Games #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Game Theory and Applications #Sports Analytics and Performance
paper · pdf · doi:10.48550/arxiv.2309.02223
openalex publication_date 2023/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Symmetric strategy improvement is an algorithm introduced by Schewe et al. (ICALP 2015) that can be used to solve two-player games on directed graphs such as parity games and mean payoff games. In contrast to the usual well-known strategy improvement algorithm, it iterates over strategies of both players simultaneously. The symmetric version solves the known worst-case examples for strategy improvement quickly, however its worst-case complexity remained open. We present a class of worst-case examples for symmetric strategy improvement on which this symmetric version also takes exponentially many steps. Remarkably, our examples exhibit this behaviour for any choice of improvement rule, which is in contrast to classical strategy improvement where hard instances are usually hand-crafted for a specific improvement rule. We present a generalized version of symmetric strategy iteration depending less rigidly on the interplay of the strategies of both players. However, it turns out it has the same shortcomings.