Spontaneous emergence of groups and signaling diversity in dynamic networks

TL;DR

The study addresses how signaling and social structure coevolve in populations where agents can choose partners. It combines a Lewis $2\\times2\\times2$ sender-receiver game with dynamic networks and Roth-Erev reinforcement learning to reveal endogenous grouping, including two homogeneous signaling systems and a robust hybrid group (S1R2–S2R1) that coordinates with complementary types while hindering information leakage. The hybrid groups form bipartite-like networks, enabling fast initial information diffusion but slower full spread, and yield mutual information between signal and action near zero, making them opaque to outsiders. The results are robust across parameter settings and extend to larger state-spaces, offering testable predictions about signaling diversity and network architecture in common-interest signaling.

Abstract

We study the coevolution of network structure and signaling behavior. We model agents who can preferentially associate with others in a dynamic network while they also learn to play a simple sender-receiver game. We have four major findings. First, signaling interactions in dynamic networks are sufficient to cause the endogenous formation of distinct signaling groups, even in an initially homogeneous population. Second, dynamic networks allow the emergence of novel {\em hybrid} signaling groups that do not converge on a single common signaling system but are instead composed of different yet complementary signaling strategies. We show that the presence of these hybrid groups promotes stable diversity in signaling among other groups in the population. Third, we find important distinctions in information processing capacity of different groups: hybrid groups diffuse information more quickly initially but at the cost of taking longer to reach all group members. Fourth, our findings pertain to all common interest signaling games, are robust across many parameters, and mitigate known problems of inefficient communication.

Figures (9)

• Figure 1: Different strategies to achieve signal coordination. a)Homogeneous signaling (top): complement strategies match. Hybrid signaling: complement strategies differ. Agents using hybrid strategies can coordinate successfully with complementary types, but they take the wrong action if when interacting with themselves (red circles). b) Homogeneous agents interact optimally with any agent using the same strategy, while hybrid agents only interact optimally with the complementary types (solid black arrows). Interactions between the hybrid types and the homogeneous types receive non-zero payoffs, but are nearly eliminated by the end of the simulation (dashed arrows).
• Figure 2: Game play and updating mechanism. In each round agents must (1) select an interaction partner, (2) earn a payoff based on the expected outcome, and (3) update their network and strategy weights based on the payoff.
• Figure 3: Emergence of Signaling Groups.a) Example outcome from one simulation of the $2\times2\times2$ game using force-directed layout. Inner and outer node colors represent an agents primary sender and receiver strategy. Inset. Population starts from uniform network ties and strategy weights. Main. Population separates into three clusters: two homogeneous and one hybrid (dashed lines). Agents in the hybrid group form a bi-partite network and interact only with those of opposite type (for visual clarity links with less than 1% interaction probability are not shown). b) Each bar represent one simulation containing 100 agents. Bars are sorted by the size of hybrid group. 87% contain a hybrid group (S1R2-S2R1) and many simulation runs contain all three groups.
• Figure S1: Network Properties. a) Despite most agents having a strongly preferred partner at any point in time, the identity of this partner frequently cycles among compatible partners. In most cases agents settle on a preferred strategy before identifying compatible partners for that strategy. b) While the structure of hybrid and homogeneous networks differ, many of the their properties are the same. Agents in each type of group maintain similarly large average interaction probabilities with their preferred partner.
• Figure S2: Group Size by Type. a) The distribution of group sizes demonstrates that while the presence of hybrid groups is more robust, they tend to be smaller in size than their homogeneous counterparts. Furthermore, no population converges to a single hybrid group, despite this being a relatively common outcome for homogeneous groups. b) Faster network learning increases the size of hybrid groups who must overcome additional constraints in their network structure. Faster network learning also decreases the likelihood that any group type fails to form in a given population. This is because agents are able to more quickly sort themselves into insular groups enabling more strategy diversity. For visual clarity we plot only the distribution of S1R1 groups and not S2R2 groups, because as expected their distributions are nearly identical.