# Pure Strategy Best Responses to Mixed Strategies in Repeated Games

arXiv: https://arxiv.org/abs/1902.09066 · HTML: https://mlsanity.com/paper/1902.09066/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2019.

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

- [Constant-Memory Strategies in Stochastic Games: Best Responses and Equilibria](https://mlsanity.com/paper/2505.07008/) (2025)

## Abstract (arXiv)

Repeated games are difficult to analyze, especially when agents play mixed strategies. We study one-memory strategies in iterated prisoner's dilemma, then generalize the result to k-memory strategies in repeated games. Our result shows that there always exists a pure strategy best response, which can be computed with SMT or MDP solvers. However, there may not exist such pure strategy best response in multi-agent tournaments. All source code is released for verification.