# Dynamics and Convergences for Markov Coevolutionary Opinion Formation Games in Dynamic Social Networks

arXiv: https://arxiv.org/abs/2607.05580 · HTML: https://mlsanity.com/paper/2607.05580/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Multi-agent reinforcement learning, one of 15 directions in Deep reinforcement learning methods.
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Placed in

- Deep reinforcement learning methods / [Multi-agent reinforcement learning](https://mlsanity.com/deeprl/multi-agent-reinforcement-learning/)

## Builds on (most cited first, 10 of 10)

- [On the Theory of Policy Gradient Methods: Optimality, Approximation, and Distribution Shift](https://mlsanity.com/paper/1908.00261/) (2019)
- [Independent Policy Gradient Methods for Competitive Reinforcement Learning](https://mlsanity.com/paper/2101.04233/) (2021)
- [Global Convergence of Multi-Agent Policy Gradient in Markov Potential Games](https://mlsanity.com/paper/2106.01969/) (2021)
- [On the convergence of single-call stochastic extra-gradient methods](https://mlsanity.com/paper/1908.08465/) (2019)
- [Last-iterate Convergence of Decentralized Optimistic Gradient Descent/Ascent in Infinite-horizon Competitive Markov Games](https://mlsanity.com/paper/2102.04540/) (2021)
- [Tight last-iterate convergence rates for no-regret learning in multi-player games](https://mlsanity.com/paper/2010.13724/) (2020)
- [Decoding Echo Chambers: LLM-Powered Simulations Revealing Polarization in Social Networks](https://mlsanity.com/paper/2409.19338/) (2024)
- [On Last-Iterate Convergence Beyond Zero-Sum Games](https://mlsanity.com/paper/2203.12056/) (2022)
- [Near-Optimal Policy Optimization for Correlated Equilibrium in General-Sum Markov Games](https://mlsanity.com/paper/2401.15240/) (2024)
- [Bounds on the Price of Anarchy for a More General Class of Directed Graphs in Opinion Formation Games](https://mlsanity.com/paper/1602.02527/) (2016)

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

- [Agent-based Modeling: Equilibrium, Echo Chambers, and Efficiency in Hybrid Coevolutionary Opinion Games](https://mlsanity.com/paper/2609.27639/) (2026)

## Abstract (arXiv)

While deterministic variants of the coevolutionary opinion formation games such as the K-Nearest Neighbor (K-NN) game, e.g., in Bhawalkar et al., in a dynamic social network can sometimes be shown to stabilize using potential functions or localized smoothness arguments, introducing stochasticity fundamentally changes the mathematical landscape. In the "K-NN Markov game", network topologies evolve via a time-varying, randomized selection process. Proving whether such a system, as a special case of general-sum Markov games, converges to an equilibrium is a profoundly non-obvious and challenging theoretical question. Multiagent reinforcement learning has been shown to derive Nash (minimax) equilibria in two-player zero-sum Markov games and Markov potential games (along with some price-of-anarchy types of results). In recent work, optimistic dynamics are shown to converge to correlated equilibria in general-sum Markov games while the price-of-anarchy bounds are unknown. We thus analyze playing specific no-regret algorithms in general-sum Markov games for convergence to a stricter set than correlated equilibria. We integrate the convergence analysis techniques from multi-agent reinforcement learning in works of Wei et al. and online learning in a recent work of Anagnostides et al. Specifically in (general-sum) Markov games, since the regret of the optimistic gradient ascent algorithm would have extra positive terms coming from Q-values, taking care of these terms requires non-trivial extra work setting an appropriate range of our learning rate and deriving the threshold on the number of iterations for convergence or a bounded price of anarchy, significantly different from those in the assumption in a main technical theorem of Anagnostides et al. We analyze a weaker sense of convergences to approximate Nash equilibria by playing optimistic gradient ascents in general-sum Markov games.