# On the Global Convergence of Stochastic Fictitious Play in Stochastic Games with Turn-based Controllers

arXiv: https://arxiv.org/abs/2204.01382 · HTML: https://mlsanity.com/paper/2204.01382/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2022.

## Built on by (most cited first, 3 of 3)

- [Multi-Player Zero-Sum Markov Games with Networked Separable Interactions](https://mlsanity.com/paper/2307.09470/) (2023)
- [A Nonparametric Approach with Marginals for Modeling Consumer Choice](https://mlsanity.com/paper/2208.06115/) (2022)
- [Grouped Satisficing Paths in Pure Strategy Games: a Topological Perspective](https://mlsanity.com/paper/2509.23157/) (2025)

## Abstract (arXiv)

This paper presents a learning dynamic with almost sure convergence guarantee for any stochastic game with turn-based controllers (on state transitions) as long as stage-payoffs induce a zero-sum or identical-interest game. Stage-payoffs for different states can even have different structures, e.g., by summing to zero in some states and being identical in others. The dynamics presented combines the classical stochastic fictitious play with value iteration for stochastic games. There are two key properties: (i) players play finite horizon stochastic games with increasing lengths within the underlying infinite-horizon stochastic game, and (ii) the turn-based controllers ensure that the auxiliary stage-games (induced from the continuation payoff estimated) are strategically equivalent to zero-sum or identical-interest games.