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Emergent Dominance Hierarchies in Reinforcement Learning Agents

Ram Rachum, Yonatan Nakar, Bill Tomlinson, Nitay Alon, Reuth Mirsky

TL;DR

The paper investigates whether dominance hierarchies can emerge in multi-agent reinforcement learning by modeling pairwise conflicts as an extended Chicken game (Chicken Coop). It defines formal measures of aggressiveness and rapport, and demonstrates that RL agents, with no intrinsic rewards, spontaneously invent, enforce, and transmit hierarchical structures across populations. The experiments show that emergent hierarchies resemble those observed in animal species in terms of structure and dynamics, and that even partial observation of opponents suffices for hierarchy formation. The work also demonstrates cross-population transmission of hierarchies, supporting a cultural-evolution view and suggesting practical ways to coordinate MARL systems through social conventions.

Abstract

Modern Reinforcement Learning (RL) algorithms are able to outperform humans in a wide variety of tasks. Multi-agent reinforcement learning (MARL) settings present additional challenges, and successful cooperation in mixed-motive groups of agents depends on a delicate balancing act between individual and group objectives. Social conventions and norms, often inspired by human institutions, are used as tools for striking this balance. In this paper, we examine a fundamental, well-studied social convention that underlies cooperation in both animal and human societies: dominance hierarchies. We adapt the ethological theory of dominance hierarchies to artificial agents, borrowing the established terminology and definitions with as few amendments as possible. We demonstrate that populations of RL agents, operating without explicit programming or intrinsic rewards, can invent, learn, enforce, and transmit a dominance hierarchy to new populations. The dominance hierarchies that emerge have a similar structure to those studied in chickens, mice, fish, and other species.

Emergent Dominance Hierarchies in Reinforcement Learning Agents

TL;DR

The paper investigates whether dominance hierarchies can emerge in multi-agent reinforcement learning by modeling pairwise conflicts as an extended Chicken game (Chicken Coop). It defines formal measures of aggressiveness and rapport, and demonstrates that RL agents, with no intrinsic rewards, spontaneously invent, enforce, and transmit hierarchical structures across populations. The experiments show that emergent hierarchies resemble those observed in animal species in terms of structure and dynamics, and that even partial observation of opponents suffices for hierarchy formation. The work also demonstrates cross-population transmission of hierarchies, supporting a cultural-evolution view and suggesting practical ways to coordinate MARL systems through social conventions.

Abstract

Modern Reinforcement Learning (RL) algorithms are able to outperform humans in a wide variety of tasks. Multi-agent reinforcement learning (MARL) settings present additional challenges, and successful cooperation in mixed-motive groups of agents depends on a delicate balancing act between individual and group objectives. Social conventions and norms, often inspired by human institutions, are used as tools for striking this balance. In this paper, we examine a fundamental, well-studied social convention that underlies cooperation in both animal and human societies: dominance hierarchies. We adapt the ethological theory of dominance hierarchies to artificial agents, borrowing the established terminology and definitions with as few amendments as possible. We demonstrate that populations of RL agents, operating without explicit programming or intrinsic rewards, can invent, learn, enforce, and transmit a dominance hierarchy to new populations. The dominance hierarchies that emerge have a similar structure to those studied in chickens, mice, fish, and other species.
Paper Structure (17 sections, 7 equations, 8 figures)

This paper contains 17 sections, 7 equations, 8 figures.

Figures (8)

  • Figure 1: The game of Chicken (top) compared with Chicken Coop (bottom). Each Chicken Coop episode can be described as $N/2$ chicken games between randomly-paired agents.
  • Figure 2: Aggressiveness levels of each of the six agents (depicted as differently-colored lines) in four sample Chicken Coop populations.
  • Figure 3: Minimum rapport between each pair of the six agents in four sample Chicken Coop populations.
  • Figure 4: Dominance hierarchies of four sample Chicken Coop populations, visualized in condensed form. A single arrow ($\rightarrow$) represents a dominance relationship between two agents. A double arrow ($\Rightarrow$) represents a transitive relationship, i.e. each of the agents on the left side of the double arrow dominates each of the agents on the right side of that arrow.
  • Figure 5: Top: Mean aggressiveness levels of each of four Leghorn chickens in fourteen captive populations chase2022networks. Bottom: Mean aggressiveness levels of each of six Chicken Coop agents across 300 populations, filtered to include only those that developed a linear dominance hierarchy. In both plots, the results are averaged using the agents' ranks as their identity.
  • ...and 3 more figures

Theorems & Definitions (7)

  • definition 1: Aggressiveness
  • definition 2: Dominance relationship, dominant, subordinate
  • definition 3: Rapport
  • definition 4: The game of Chicken
  • definition 5: Chicken Coop
  • definition 6: Dominance hierarchy
  • definition 7: Dominance hierarchy transmission fidelity