Interactive Restless Multi-armed Bandit Game and Swarm Intelligence Effect

TL;DR

This paper investigates the emergence of swarm intelligence in an interactive restless multi-armed bandit game, identifying conditions where social learning leads to optimal collective behavior through theoretical analysis and laboratory experiments.

Contribution

It provides the first detailed analysis of conditions for swarm intelligence emergence in an interactive rMAB game, combining theoretical strategies with experimental validation.

Findings

Swarm intelligence occurs when social learning is significantly more optimal than asocial learning.

Optimal strategies depend on the payoff change probability $p_{c}$ and the number of options $n_{I}$.

Laboratory experiments confirm the theoretical predictions about when swarm intelligence emerges.

Abstract

We obtain the conditions for the emergence of the swarm intelligence effect in an interactive game of restless multi-armed bandit (rMAB). A player competes with multiple agents. Each bandit has a payoff that changes with a probability $p_{c}$ per round. The agents and player choose one of three options: (1) Exploit (a good bandit), (2) Innovate (asocial learning for a good bandit among $n_{I}$ randomly chosen bandits), and (3) Observe (social learning for a good bandit). Each agent has two parameters $(c,p_{obs})$ to specify the decision: (i) $c$, the threshold value for Exploit, and (ii) $p_{obs}$, the probability for Observe in learning. The parameters $(c,p_{obs})$ are uniformly distributed. We determine the optimal strategies for the player using complete knowledge about the rMAB. We show whether or not social or asocial learning is more optimal in the $(p_{c},n_{I})$ space and define the swarm intelligence effect. We conduct a laboratory experiment (67 subjects) and observe the swarm intelligence effect only if $(p_{c},n_{I})$ are chosen so that social learning is far more optimal than asocial learning.