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

arXiv: https://arxiv.org/abs/2305.19158 · HTML: https://mlsanity.com/paper/2305.19158/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 66 references that are in the map.
- First posted on arXiv 30 May 2023.

## Builds on (most cited first, 30 of 36)

- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [Causal Bandits: Learning Good Interventions via Causal Inference](https://mlsanity.com/paper/1606.03203/) (2016)
- [Linear Contextual Bandits with Knapsacks](https://mlsanity.com/paper/1507.06738/) (2015)
- [Cascading Bandits: Learning to Rank in the Cascade Model](https://mlsanity.com/paper/1502.02763/) (2015)
- [Competing Bandits in Matching Markets](https://mlsanity.com/paper/1906.05363/) (2019)
- [SIC-MMAB: Synchronisation Involves Communication in Multiplayer Multi-Armed Bandits](https://mlsanity.com/paper/1809.08151/) (2018)
- [Bandit Learning in Decentralized Matching Markets](https://mlsanity.com/paper/2012.07348/) (2020)
- [Modeling Content Creator Incentives on Algorithm-Curated Platforms](https://mlsanity.com/paper/2206.13102/) (2022)
- [Learning Equilibria in Matching Markets from Bandit Feedback](https://mlsanity.com/paper/2108.08843/) (2021)
- [A Game-Theoretic Approach to Recommendation Systems with Strategic Content Providers](https://mlsanity.com/paper/1806.00955/) (2018)
- [Supply-Side Equilibria in Recommender Systems](https://mlsanity.com/paper/2206.13489/) (2022)
- [Beyond log2(T) Regret for Decentralized Bandits in Matching Markets](https://mlsanity.com/paper/2103.07501/) (2021)
- [How Bad is Top-K Recommendation under Competing Content Creators?](https://mlsanity.com/paper/2302.01971/) (2023)
- [Decentralized Multi-player Multi-armed Bandits with No Collision Information](https://mlsanity.com/paper/2003.00162/) (2020)
- [Multiplayer bandits without observing collision information](https://mlsanity.com/paper/1808.08416/) (2018)
- [A survey on multi-player bandits](https://mlsanity.com/paper/2211.16275/) (2022)
- [Heterogeneous Multi-player Multi-armed Bandits: Closing the Gap and Generalization](https://mlsanity.com/paper/2110.14622/) (2021)
- [Selfish Robustness and Equilibria in Multi-Player Bandits](https://mlsanity.com/paper/2002.01197/) (2020)
- [Multiplayer Bandit Learning, from Competition to Cooperation](https://mlsanity.com/paper/1908.01135/) (2019)
- [Towards Optimal Algorithms for Multi-Player Bandits without Collision Sensing Information](https://mlsanity.com/paper/2103.13059/) (2021)
- [Decentralized Heterogeneous Multi-Player Multi-Armed Bandits with Non-Zero Rewards on Collisions](https://mlsanity.com/paper/1910.09089/) (2019)
- [Multi-Player Multi-Armed Bandits with Finite Shareable Resources Arms: Learning Algorithms & Applications](https://mlsanity.com/paper/2204.13502/) (2022)
- [Multi-User Multi-Armed Bandits for Uncoordinated Spectrum Access](https://mlsanity.com/paper/1807.00867/) (2018)
- [From Recommendation Systems to Facility Location Games](https://mlsanity.com/paper/1809.02931/) (2018)
- [Multi-player Multi-armed Bandits with Collision-Dependent Reward Distributions](https://mlsanity.com/paper/2106.13669/) (2021)
- [Online Learning in a Creator Economy](https://mlsanity.com/paper/2305.11381/) (2023)
- [Resource Allocation in NOMA-based Self-Organizing Networks using Stochastic Multi-Armed Bandits](https://mlsanity.com/paper/2101.06340/) (2021)
- [An Instance-Dependent Analysis for the Cooperative Multi-Player Multi-Armed Bandit](https://mlsanity.com/paper/2111.04873/) (2021)
- [Multiple-Play Stochastic Bandits with Shareable Finite-Capacity Arms](https://mlsanity.com/paper/2206.08776/) (2022)
- [Convergence of Learning Dynamics in Information Retrieval Games](https://mlsanity.com/paper/1806.05359/) (2018)

## Built on by (most cited first, 6 of 6)

- [Optimistic Thompson Sampling for No-Regret Learning in Unknown Games](https://mlsanity.com/paper/2402.09456/) (2024)
- [Heterogeneous Data Game: Characterizing the Model Competition Across Multiple Data Sources](https://mlsanity.com/paper/2505.07688/) (2025)
- [PPA-Game: Characterizing and Learning Competitive Dynamics Among Online Content Creators](https://mlsanity.com/paper/2403.15524/) (2024)
- [Competitive Multi-armed Bandit Games for Resource Sharing](https://mlsanity.com/paper/2503.20975/) (2025)
- [Decentralized Asynchronous Multi-player Bandits](https://mlsanity.com/paper/2509.25824/) (2025)
- [Multiple-play Stochastic Bandits with Prioritized Arm Capacity Sharing](https://mlsanity.com/paper/2512.21626/) (2025)

## Abstract (arXiv)

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.