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A Framework for Exploring Social Interactions in Multiagent Decision-Making for Two-Queue Systems

Mallory E. Gaspard, Naomi Ehrich Leonard

Abstract

We introduce a new framework for multiagent decision-making in queueing systems that leverages the agility and robustness of nonlinear opinion dynamics to break indecision during queue selection and to capture the influence of social interactions on collective behavior. Queueing models are central to understanding multiagent behavior in service settings. Many prior models assume that each agent's decision-making process is optimization-based and governed by rational responses to changes in the queueing system. Instead, we introduce an internal opinion state, driven by nonlinear opinion dynamics, that represents the evolving strength of the agent's preference between two available queues. The opinion state is influenced by social interactions, which can modify purely rational responses. We propose a new subclass of queueing models in which each agent's behavioral decisions (e.g., joining or switching queues) are determined by this evolving opinion state. We prove a sufficient parameter condition that guarantees the Markov chain describing the evolving opinion and queueing system states reaches the Nash equilibrium of an underlying congestion game in finite expected time. We then explore the richness of the new framework through numerical simulations that illustrate the role of social interactions and an individual's access to system information in shaping collective behavior.

A Framework for Exploring Social Interactions in Multiagent Decision-Making for Two-Queue Systems

Abstract

We introduce a new framework for multiagent decision-making in queueing systems that leverages the agility and robustness of nonlinear opinion dynamics to break indecision during queue selection and to capture the influence of social interactions on collective behavior. Queueing models are central to understanding multiagent behavior in service settings. Many prior models assume that each agent's decision-making process is optimization-based and governed by rational responses to changes in the queueing system. Instead, we introduce an internal opinion state, driven by nonlinear opinion dynamics, that represents the evolving strength of the agent's preference between two available queues. The opinion state is influenced by social interactions, which can modify purely rational responses. We propose a new subclass of queueing models in which each agent's behavioral decisions (e.g., joining or switching queues) are determined by this evolving opinion state. We prove a sufficient parameter condition that guarantees the Markov chain describing the evolving opinion and queueing system states reaches the Nash equilibrium of an underlying congestion game in finite expected time. We then explore the richness of the new framework through numerical simulations that illustrate the role of social interactions and an individual's access to system information in shaping collective behavior.

Paper Structure

This paper contains 8 sections, 4 theorems, 22 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Opinion-Driven Selection Between Two Queues
  3. Nonlinear Opinion Dynamics
  4. Agent Based Opinion-Driven Queueing Model
  5. Queue Selection and Congestion Games
  6. Sufficient Condition for Hitting the Set of Nash Configurations in Finite Time
  7. Numerical Experiments
  8. Conclusion and Future Directions

Key Result

Proposition 1

Consider a congestion game where $N$ agents are choosing between two queues with identical resource costs, $c_A = c_B = c(\cdot)$. A queue membership configuration $(n_A, n_B)$ is a Nash equilibrium if and only if $|n_A - n_B| \leq 1$.

Figures (2)

  • Figure 1: Queue lengths (left) and per-agent opinions (right) over time for $10$ anti-cooperative agents. $6$ agents lack queue imbalance information. Agents polarize quickly, do not switch queues, and easily settle in $\mathcal{N}$.
  • Figure 2: Queue lengths (left) and per-agent opinions (right) over time for $10$ fully-cooperative agents when $6$ agents lack imbalance information. After initial herding near $t = 4$ where all agents end up in $A$, the agents rapidly settle into two distinct groups based on their access to imbalance information.

Theorems & Definitions (10)

  • Definition 1: Queue Selection Congestion Game
  • Proposition 1
  • proof
  • Definition 2: Nash Configuration Band
  • Lemma 1: Input Sign Alignment with the Cheaper Queue
  • proof
  • Lemma 2: Uniform Opinion Magnitude Bound
  • proof
  • Theorem 1: Nash Hitting in Finite Expected Time
  • proof