Stochastic Games with Limited Public Memory
Kristoffer Arnsfelt Hansen, Rasmus Ibsen-Jensen, Abraham Neyman

TL;DR
This paper proves that near-optimal strategies in two-player zero-sum stochastic games can be implemented with logarithmic memory, significantly improving previous bounds, but such strategies cannot be achieved with bounded public memory.
Contribution
It establishes that uniform ε-optimal strategies require only O(log n) memory states, and demonstrates the limitations of bounded public memory strategies in such games.
Findings
Near-optimal strategies use at most O(log n) memory states.
Time-independent strategies can achieve near-optimality with high probability.
Bounded public memory strategies cannot guarantee near-optimal payoffs in the Big Match.
Abstract
We study the memory resources required for near-optimal play in two-player zero-sum stochastic games with the long-run average payoff. Although optimal strategies may not exist in such games, near-optimal strategies always do. Mertens and Neyman (1981) proved that in any stochastic game, for any , there exist uniform -optimal memory-based strategies -- i.e., strategies that are -optimal in all sufficiently long -stage games -- that use at most memory states within the first stages. We improve this bound on the number of memory states by proving that in any stochastic game, for any , there exist uniform -optimal memory-based strategies that use at most memory states in the first stages. Moreover, we establish the existence of uniform -optimal memory-based strategies whose…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGame Theory and Applications · Opinion Dynamics and Social Influence
