# A Game-Theoretic Analysis of the Off-Switch Game

arXiv: https://arxiv.org/abs/1708.03871 · HTML: https://mlsanity.com/paper/1708.03871/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2017.

## Built on by (most cited first, 8 of 8)

- [The Shutdown Problem: An AI Engineering Puzzle for Decision Theorists](https://mlsanity.com/paper/2403.04471/) (2024)
- [Impossibility Results in AI: A Survey](https://mlsanity.com/paper/2109.00484/) (2021)
- [The Partially Observable Off-Switch Game](https://mlsanity.com/paper/2411.17749/) (2024)
- [Core Safety Values for Provably Corrigible Agents](https://mlsanity.com/paper/2507.20964/) (2025)
- [Towards Shutdownable Agents via Stochastic Choice](https://mlsanity.com/paper/2407.00805/) (2024)
- [Misalignment from Treating Means as Ends](https://mlsanity.com/paper/2507.10995/) (2025)
- [Towards Shutdownable Agents: Generalizing Stochastic Choice in RL Agents and LLMs](https://mlsanity.com/paper/2604.17502/) (2026)
- [The AI off-switch problem as a signalling game: bounded rationality and incomparability](https://mlsanity.com/paper/2502.06403/) (2025)

## Abstract (arXiv)

The off-switch game is a game theoretic model of a highly intelligent robot interacting with a human. In the original paper by Hadfield-Menell et al. (2016), the analysis is not fully game-theoretic as the human is modelled as an irrational player, and the robot's best action is only calculated under unrealistic normality and soft-max assumptions. In this paper, we make the analysis fully game theoretic, by modelling the human as a rational player with a random utility function. As a consequence, we are able to easily calculate the robot's best action for arbitrary belief and irrationality assumptions.