# Recursive Joint Simulation in Games

arXiv: https://arxiv.org/abs/2402.08128 · HTML: https://mlsanity.com/paper/2402.08128/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 55 references that are in the map.
- First posted on arXiv 12 Feb 2024.

## Builds on (most cited first, 5 of 5)

- [Robust Cooperation in the Prisoner's Dilemma: Program Equilibrium via Provability Logic](https://mlsanity.com/paper/1401.5577/) (2014)
- [Game Theory with Simulation of Other Players](https://mlsanity.com/paper/2305.11261/) (2023)
- [Cooperative and uncooperative institution designs: Surprises and problems in open-source game theory](https://mlsanity.com/paper/2208.07006/) (2022)
- [Game Theory with Translucent Players](https://mlsanity.com/paper/1310.6438/) (2013)
- [A Note on the Compatibility of Different Robust Program Equilibria of the Prisoner's Dilemma](https://mlsanity.com/paper/2211.05057/) (2022)

## Built on by (most cited first, 4 of 4)

- [CoopEval: Benchmarking Cooperation-Sustaining Mechanisms and LLM Agents in Social Dilemmas](https://mlsanity.com/paper/2604.15267/) (2026)
- [Imperfect-Recall Games: Equilibrium Concepts and Their Complexity](https://mlsanity.com/paper/2406.15970/) (2024)
- [A dataset of questions on decision-theoretic reasoning in Newcomb-like problems](https://mlsanity.com/paper/2411.10588/) (2024)
- [Decision Making under Imperfect Recall: Algorithms and Benchmarks](https://mlsanity.com/paper/2602.15252/) (2026)

## Abstract (arXiv)

Game-theoretic dynamics between AI agents could differ from traditional human-human interactions in various ways. One such difference is that it may be possible to accurately simulate an AI agent, for example because its source code is known. Such an agent would then be fundamentally uncertain whether it is in the real world or in a simulation. Our aim is to explore ways of leveraging this possibility to achieve more cooperative outcomes in strategic settings. In this paper, we study an interaction between AI agents where the agents run a recursive joint simulation. That is, the agents first jointly observe a simulation of the situation they face. This simulation in turn recursively includes additional simulations (with a small chance of failure, to avoid infinite recursion), and the results of all these nested simulations are observed before an action is chosen. We show that the resulting interaction is strategically equivalent to an infinitely repeated version of the original game, allowing a direct transfer of existing results such as the various folk theorems. As evidence that the equivalence is robust, we show that it holds even when we relax some of the assumptions and that it also holds ``from the inside'' -- meaning, for an agent that finds itself inside the game and has self-locating uncertainty.