# Game Theory with Simulation in the Presence of Unpredictable Randomisation

arXiv: https://arxiv.org/abs/2410.14311 · HTML: https://mlsanity.com/paper/2410.14311/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 26 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Builds on (most cited first, 7 of 7)

- [Model evaluation for extreme risks](https://mlsanity.com/paper/2305.15324/) (2023)
- [Open Problems in Cooperative AI](https://mlsanity.com/paper/2012.08630/) (2020)
- [Game Theory with Simulation of Other Players](https://mlsanity.com/paper/2305.11261/) (2023)
- [Game Theory with Translucent Players](https://mlsanity.com/paper/1310.6438/) (2013)
- [Translucent Players: Explaining Cooperative Behavior in Social Dilemmas](https://mlsanity.com/paper/1410.3363/) (2014)
- [Simultaneous games with purchase of randomly supplied perfect information: Oracle Games](https://mlsanity.com/paper/2002.08309/) (2020)
- [Computing Optimal Commitments to Strategies and Outcome-Conditional Utility Transfers](https://mlsanity.com/paper/2402.06626/) (2024)

## Built on by (most cited first, 3 of 3)

- [AI Testing Should Account for Sophisticated Strategic Behaviour](https://mlsanity.com/paper/2508.14927/) (2025)
- [Behavioral Consistency Validation for LLM Agents: An Analysis of Trading-Style Switching through Stock-Market Simulation](https://mlsanity.com/paper/2602.07023/) (2026)
- [Decision Making under Imperfect Recall: Algorithms and Benchmarks](https://mlsanity.com/paper/2602.15252/) (2026)

## Abstract (arXiv)

AI agents will be predictable in certain ways that traditional agents are not. Where and how can we leverage this predictability in order to improve social welfare? We study this question in a game-theoretic setting where one agent can pay a fixed cost to simulate the other in order to learn its mixed strategy. As a negative result, we prove that, in contrast to prior work on pure-strategy simulation, enabling mixed-strategy simulation may no longer lead to improved outcomes for both players in all so-called "generalised trust games". In fact, mixed-strategy simulation does not help in any game where the simulatee's action can depend on that of the simulator. We also show that, in general, deciding whether simulation introduces Pareto-improving Nash equilibria in a given game is NP-hard. As positive results, we establish that mixed-strategy simulation can improve social welfare if the simulator has the option to scale their level of trust, if the players face challenges with both trust and coordination, or if maintaining some level of privacy is essential for enabling cooperation.