# Game Theory with Simulation of Other Players

arXiv: https://arxiv.org/abs/2305.11261 · HTML: https://mlsanity.com/paper/2305.11261/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2023.

## Built on by (most cited first, 13 of 13)

- [Is Your LLM Overcharging You? Tokenization, Transparency, and Incentives](https://mlsanity.com/paper/2505.21627/) (2025)
- [Cooperative AI via Decentralized Commitment Devices](https://mlsanity.com/paper/2311.07815/) (2023)
- [AI Testing Should Account for Sophisticated Strategic Behaviour](https://mlsanity.com/paper/2508.14927/) (2025)
- [The Computational Complexity of Single-Player Imperfect-Recall Games](https://mlsanity.com/paper/2305.17805/) (2023)
- [Evaluating LLMs in Open-Source Games](https://mlsanity.com/paper/2512.00371/) (2025)
- [Algorithmic Persuasion Through Simulation](https://mlsanity.com/paper/2311.18138/) (2023)
- [Recursive Joint Simulation in Games](https://mlsanity.com/paper/2402.08128/) (2024)
- [Imperfect-Recall Games: Equilibrium Concepts and Their Complexity](https://mlsanity.com/paper/2406.15970/) (2024)
- [Computing Game Symmetries and Equilibria That Respect Them](https://mlsanity.com/paper/2501.08905/) (2025)
- [Game Theory with Simulation in the Presence of Unpredictable Randomisation](https://mlsanity.com/paper/2410.14311/) (2024)
- [A game theory for foundation models shows new paths to rational cooperation through similarity inference](https://mlsanity.com/paper/2608.03958/) (2026)
- [Policy-Conditioned Policies for Multi-Agent Task Solving](https://mlsanity.com/paper/2512.21024/) (2025)
- [Decision Making under Imperfect Recall: Algorithms and Benchmarks](https://mlsanity.com/paper/2602.15252/) (2026)

## Abstract (arXiv)

Game-theoretic interactions with AI agents could differ from traditional human-human interactions in various ways. One such difference is that it may be possible to simulate an AI agent (for example because its source code is known), which allows others to accurately predict the agent's actions. This could lower the bar for trust and cooperation. In this paper, we formalize games in which one player can simulate another at a cost. We first derive some basic properties of such games and then prove a number of results for them, including: (1) introducing simulation into generic-payoff normal-form games makes them easier to solve; (2) if the only obstacle to cooperation is a lack of trust in the possibly-simulated agent, simulation enables equilibria that improve the outcome for both agents; and however (3) there are settings where introducing simulation results in strictly worse outcomes for both players.