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On the Complexity of Learning to Cooperate with Populations of Socially Rational Agents

Robert Loftin, Saptarashmi Bandyopadhyay, Mustafa Mert Çelikok

TL;DR

The paper tackles zero-shot cooperation with populations of socially rational agents in finitely repeated two-player general-sum games with private utilities. It introduces the notion of social intelligence as a combination of Hannan-consistency and cooperative compatibility, and proposes imitate-then-commit as a data-driven strategy to learn cooperation from population interactions. The authors derive lower bounds showing impossibility under certain combinations of consistency and compatibility, and provide upper bounds via imitation-based learning that outperform naive imitation. These results yield principled sample-complexity guarantees and offer insights for robust zero-shot coordination and AI alignment in heterogeneous agent ecosystems.

Abstract

Artificially intelligent agents deployed in the real-world will require the ability to reliably \textit{cooperate} with humans (as well as other, heterogeneous AI agents). To provide formal guarantees of successful cooperation, we must make some assumptions about how partner agents could plausibly behave. Any realistic set of assumptions must account for the fact that other agents may be just as adaptable as our agent is. In this work, we consider the problem of cooperating with a \textit{population} of agents in a finitely-repeated, two player general-sum matrix game with private utilities. Two natural assumptions in such settings are that: 1) all agents in the population are individually rational learners, and 2) when any two members of the population are paired together, with high-probability they will achieve at least the same utility as they would under some Pareto efficient equilibrium strategy. Our results first show that these assumptions alone are insufficient to ensure \textit{zero-shot} cooperation with members of the target population. We therefore consider the problem of \textit{learning} a strategy for cooperating with such a population using prior observations its members interacting with one another. We provide upper and lower bounds on the number of samples needed to learn an effective cooperation strategy. Most importantly, we show that these bounds can be much stronger than those arising from a "naive'' reduction of the problem to one of imitation learning.

On the Complexity of Learning to Cooperate with Populations of Socially Rational Agents

TL;DR

The paper tackles zero-shot cooperation with populations of socially rational agents in finitely repeated two-player general-sum games with private utilities. It introduces the notion of social intelligence as a combination of Hannan-consistency and cooperative compatibility, and proposes imitate-then-commit as a data-driven strategy to learn cooperation from population interactions. The authors derive lower bounds showing impossibility under certain combinations of consistency and compatibility, and provide upper bounds via imitation-based learning that outperform naive imitation. These results yield principled sample-complexity guarantees and offer insights for robust zero-shot coordination and AI alignment in heterogeneous agent ecosystems.

Abstract

Artificially intelligent agents deployed in the real-world will require the ability to reliably \textit{cooperate} with humans (as well as other, heterogeneous AI agents). To provide formal guarantees of successful cooperation, we must make some assumptions about how partner agents could plausibly behave. Any realistic set of assumptions must account for the fact that other agents may be just as adaptable as our agent is. In this work, we consider the problem of cooperating with a \textit{population} of agents in a finitely-repeated, two player general-sum matrix game with private utilities. Two natural assumptions in such settings are that: 1) all agents in the population are individually rational learners, and 2) when any two members of the population are paired together, with high-probability they will achieve at least the same utility as they would under some Pareto efficient equilibrium strategy. Our results first show that these assumptions alone are insufficient to ensure \textit{zero-shot} cooperation with members of the target population. We therefore consider the problem of \textit{learning} a strategy for cooperating with such a population using prior observations its members interacting with one another. We provide upper and lower bounds on the number of samples needed to learn an effective cooperation strategy. Most importantly, we show that these bounds can be much stronger than those arising from a "naive'' reduction of the problem to one of imitation learning.
Paper Structure (24 sections, 9 theorems, 27 equations, 1 table)

This paper contains 24 sections, 9 theorems, 27 equations, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Repeated bi-matrix games with private types.
  4. Consistency
  5. Cooperative compatibility
  6. Socially intelligent agents
  7. Coordination protocols
  8. Learning to Cooperate
  9. Altruistic Regret
  10. Consistency without Compatibility
  11. Compatibility without consistency
  12. Lower bound for socially intelligent populations
  13. Upper bound for socially intelligent populations
  14. Imitation learning.
  15. Imitate-then-commit strategy.
  16. ...and 9 more sections

Key Result

Lemma 2.4

For any $\delta, T > 0$, if both players follow strategy $s(\boldsymbol{\theta})$ at each stage, then with probability at least $1 - \delta$ we have

Theorems & Definitions (13)

  • Definition 2.1: Consistency
  • Definition 2.2: Compatibility
  • Definition 2.3: Social Intelligence
  • Lemma 2.4
  • Theorem 2.5
  • Definition 3.1: Altruistic Regret
  • Lemma 3.2
  • Theorem 3.3
  • Theorem 3.4
  • Theorem 3.5
  • ...and 3 more