Solving Imperfect-Recall Games via Sum-of-Squares Optimization

A team of researchers from academia has published a breakthrough paper on arXiv titled 'Solving Imperfect-Recall Games via Sum-of-Squares Optimization,' introducing a novel computational framework for tackling imperfect-recall extensive-form games (IREFGs). Unlike traditional game theory models that assume perfect recall (where players remember all past information), IREFGs model real-world scenarios where agents may forget parts of their history—a setting where equilibrium computation has been provably hard. The researchers propose using sum-of-squares (SOS) hierarchies to compute ex-ante optimal strategies in single-player IREFGs and Nash equilibria in multi-player settings, working directly with behavioral strategies rather than simplifying assumptions.

The theoretical results demonstrate three key advances: the SOS hierarchies converge asymptotically, under genericity assumptions this convergence is finite, and in single-player non-absentminded IREFGs, convergence occurs at a finite level determined by the number of information sets. Most practically significant, the researchers identify new classes of games called (SOS)-concave and (SOS)-monotone IREFGs where the hierarchy converges at the first level. This breakthrough means equilibrium computation reduces to solving just one semidefinite program (SDP), transforming what was previously computationally intractable into a solvable optimization problem. The method opens doors for applications in AI agent design, security games, and economic modeling where imperfect memory is a realistic constraint.