# Reflective Oracles: A Foundation for Classical Game Theory

arXiv: https://arxiv.org/abs/1508.04145 · HTML: https://mlsanity.com/paper/1508.04145/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2015.

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

- [Self-Improvements in Modern Agentic Systems: A Survey](https://mlsanity.com/paper/2607.13104/) (2026)
- [From AGI to ASI](https://mlsanity.com/paper/2606.12683/) (2026)
- [Limit-Computable Grains of Truth for Arbitrary Computable Extensive-Form (Un)Known Games](https://mlsanity.com/paper/2508.16245/) (2025)
- [On the Computational Tractability of Robust Bandits](https://mlsanity.com/paper/2610.08740/) (2026)

## Abstract (arXiv)

Classical game theory treats players as special---a description of a game contains a full, explicit enumeration of all players---even though in the real world, "players" are no more fundamentally special than rocks or clouds. It isn't trivial to find a decision-theoretic foundation for game theory in which an agent's coplayers are a non-distinguished part of the agent's environment. Attempts to model both players and the environment as Turing machines, for example, fail for standard diagonalization reasons. In this paper, we introduce a "reflective" type of oracle, which is able to answer questions about the outputs of oracle machines with access to the same oracle. These oracles avoid diagonalization by answering some queries randomly. We show that machines with access to a reflective oracle can be used to define rational agents using causal decision theory. These agents model their environment as a probabilistic oracle machine, which may contain other agents as a non-distinguished part. We show that if such agents interact, they will play a Nash equilibrium, with the randomization in mixed strategies coming from the randomization in the oracle's answers. This can be seen as providing a foundation for classical game theory in which players aren't special.