# Similarity-based cooperative equilibrium

arXiv: https://arxiv.org/abs/2211.14468 · HTML: https://mlsanity.com/paper/2211.14468/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 63 references that are in the map.
- First posted on arXiv 26 Nov 2022.

## Builds on (most cited first, 11 of 11)

- [Learning with Opponent-Learning Awareness](https://mlsanity.com/paper/1709.04326/) (2017)
- [Stable Opponent Shaping in Differentiable Games](https://mlsanity.com/paper/1811.08469/) (2018)
- [On Gradient-Based Learning in Continuous Games](https://mlsanity.com/paper/1804.05464/) (2018)
- [COLA: Consistent Learning with Opponent-Learning Awareness](https://mlsanity.com/paper/2203.04098/) (2022)
- [Near-optimal Local Convergence of Alternating Gradient Descent-Ascent for Minimax Optimization](https://mlsanity.com/paper/2102.09468/) (2021)
- [Evolving intrinsic motivations for altruistic behavior](https://mlsanity.com/paper/1811.05931/) (2018)
- [Robust Cooperation in the Prisoner's Dilemma: Program Equilibrium via Provability Logic](https://mlsanity.com/paper/1401.5577/) (2014)
- [Cooperative and uncooperative institution designs: Surprises and problems in open-source game theory](https://mlsanity.com/paper/2208.07006/) (2022)
- [Normative Disagreement as a Challenge for Cooperative AI](https://mlsanity.com/paper/2111.13872/) (2021)
- [Learning in two-player games between transparent opponents](https://mlsanity.com/paper/2012.02671/) (2020)
- [Reinforcement Learning in Conflicting Environments for Autonomous Vehicles](https://mlsanity.com/paper/1610.07089/) (2016)

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

- [Principal-Agent Reinforcement Learning: Orchestrating AI Agents with Contracts](https://mlsanity.com/paper/2407.18074/) (2024)
- [Evaluating LLMs in Open-Source Games](https://mlsanity.com/paper/2512.00371/) (2025)
- [Causal Foundations of Collective Agency](https://mlsanity.com/paper/2605.00248/) (2026)
- [Identity, Incentives, and Cooperative Behavior for AI: Reverse-Engineering Multiagent Cooperation](https://mlsanity.com/paper/2610.19188/) (2026)

## Abstract (arXiv)

As machine learning agents act more autonomously in the world, they will increasingly interact with each other. Unfortunately, in many social dilemmas like the one-shot Prisoner's Dilemma, standard game theory predicts that ML agents will fail to cooperate with each other. Prior work has shown that one way to enable cooperative outcomes in the one-shot Prisoner's Dilemma is to make the agents mutually transparent to each other, i.e., to allow them to access one another's source code (Rubinstein 1998, Tennenholtz 2004) -- or weights in the case of ML agents. However, full transparency is often unrealistic, whereas partial transparency is commonplace. Moreover, it is challenging for agents to learn their way to cooperation in the full transparency setting. In this paper, we introduce a more realistic setting in which agents only observe a single number indicating how similar they are to each other. We prove that this allows for the same set of cooperative outcomes as the full transparency setting. We also demonstrate experimentally that cooperation can be learned using simple ML methods.