# A Tauberian theorem for nonexpansive operators and applications to zero-sum stochastic games

arXiv: https://arxiv.org/abs/1501.06525 · HTML: https://mlsanity.com/paper/1501.06525/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2015.

## Built on by (most cited first, 1 of 1)

- [Reinforcement Learning with Depreciating Assets](https://mlsanity.com/paper/2302.14176/) (2023)

## Abstract (arXiv)

We prove a Tauberian theorem for nonexpansive operators, and apply it to the model of zero-sum stochastic game. Under mild assumptions, we prove that the value of the lambda-discounted game v_{lambda} converges uniformly when lambda goes to 0 if and only if the value of the n-stage game v_n converges uniformly when n goes to infinity. This generalizes the Tauberian theorem of Lehrer and Sorin (1992) to the two-player zero-sum case. We also provide the first example of a stochastic game with public signals on the state and perfect observation of actions, with finite state space, signal sets and action sets, in which for some initial state k_1 known by both players, (v_{lambda}(k_1)) and (v_n(k_1)) converge to distinct limits.