Anytime-Constrained Equilibria in Polynomial Time
This provides efficient computation methods for action-constrained Markov games, which is incremental but addresses a known bottleneck in game theory.
The paper tackles the problem of computing anytime-constrained equilibria in Markov games, which is NP-hard, and presents a polynomial-time algorithm for approximate computation with optimal guarantees under P ≠ NP.
We extend anytime constraints to the Markov game setting and the corresponding solution concept of an anytime-constrained equilibrium (ACE). Then, we present a comprehensive theory of anytime-constrained equilibria that includes (1) a computational characterization of feasible policies, (2) a fixed-parameter tractable algorithm for computing ACE, and (3) a polynomial-time algorithm for approximately computing ACE. Since computing a feasible policy is NP-hard even for two-player zero-sum games, our approximation guarantees are optimal so long as $P \neq NP$. We also develop the first theory of efficient computation for action-constrained Markov games, which may be of independent interest.