Competing for Shareable Arms in Multi-Player Multi-Armed Bandits

TL;DR

This paper introduces a new multi-player multi-armed bandit model where selfish agents compete and share rewards, analyzes equilibrium strategies, and proposes an algorithm with strong theoretical guarantees validated through experiments.

Contribution

The paper models a novel competitive multi-player bandit setting with reward sharing, analyzes Nash equilibrium, and proposes SMAA with proven regret bounds and stability properties.

Findings

SMAA achieves low regret for all players.

No single player can significantly improve rewards by deviation.

The method performs well in synthetic experiments.

Abstract

Competitions for shareable and limited resources have long been studied with strategic agents. In reality, agents often have to learn and maximize the rewards of the resources at the same time. To design an individualized competing policy, we model the competition between agents in a novel multi-player multi-armed bandit (MPMAB) setting where players are selfish and aim to maximize their own rewards. In addition, when several players pull the same arm, we assume that these players averagely share the arms' rewards by expectation. Under this setting, we first analyze the Nash equilibrium when arms' rewards are known. Subsequently, we propose a novel Selfish MPMAB with Averaging Allocation (SMAA) approach based on the equilibrium. We theoretically demonstrate that SMAA could achieve a good regret guarantee for each player when all players follow the algorithm. Additionally, we establish that no single selfish player can significantly increase their rewards through deviation, nor can they detrimentally affect other players' rewards without incurring substantial losses for themselves. We finally validate the effectiveness of the method in extensive synthetic experiments.