# Best response dynamics on random graphs

arXiv: https://arxiv.org/abs/2011.12983 · HTML: https://mlsanity.com/paper/2011.12983/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2020.

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

- [Performative Prediction on Games and Mechanism Design](https://mlsanity.com/paper/2408.05146/) (2024)

## Abstract (arXiv)

We consider evolutionary games on a population whose underlying topology of interactions is determined by a binomial random graph G(n,p). Our focus is on 2-player symmetric games with 2 strategies played between the incident members of such a population. Players update their strategies synchronously. At each round, each player selects the strategy that is the best response to the current set of strategies its neighbours play. We show that such a system reduces to generalised majority and minority dynamics. We show rapid convergence to unanimity for p in a range that depends on a certain characteristic of the payoff matrix. In the presence of a bias among the pure Nash equilibria of the game, we determine a sharp threshold on p above which the largest connected component reaches unanimity with high probability. For p below this critical value, where this does not happen, we identify those substructures inside the largest component that remain discordant throughout the evolution of the system.