Analyzing Multi-Player Resource-Sharing Games with Fair Reward Allocation

Core Concepts

The authors explore resource-sharing games with fair reward allocation, focusing on worst-case expected utility maximization in two settings: one-slot and online scenarios. They develop algorithms to minimize regret and provide insights into complex problems.

Abstract

This paper delves into multi-player resource-sharing games with fair reward allocation, examining worst-case expected utility maximization in different settings. It introduces novel Upper Confidence Bound algorithms to minimize regret and offers valuable insights into solving intricate problems efficiently. The study's applications range from communication systems to market competition scenarios, showcasing the relevance of the research in various real-world contexts.

Stats

The algorithm achieves a worst-case regret of nD√T + 4np2rT log(2nrCT3(T + 1)) + 1.
Ek < ˜Ek[t] for all k, t ∈ [1 : n] × [1 : T].
Ek > ˜Ek[t] − 2s2 log T(T+1)δnk[t] ∨ 1 for all k, t ∈ [1 : n] × [1 : T].
The algorithm yields a maximum error of O(ε) when choosing β = ε and T ≥ 1/ε^2.

Quotes

Key Insights Distilled From

Multi-Player Resource-Sharing Games with Fair Reward Allocation

by Mevan Wijewa... at arxiv.org 03-05-2024

https://arxiv.org/pdf/2402.05300.pdf

Deeper Inquiries

How can the findings of this research be applied to other fields outside game theory

The findings of this research on multi-player resource-sharing games with fair reward allocation can be applied to various fields outside game theory. One potential application is in the field of communication systems, specifically in multiple access control (MAC) scenarios where channels are shared among users. By applying the concepts of fair reward allocation, such as dividing rewards equally among users selecting a channel, communication systems can optimize resource utilization and improve overall system efficiency. Additionally, these findings can be utilized in economic scenarios where firms compete for market entry or share revenue from markets. Implementing fair reward allocation models can help ensure equitable outcomes and promote healthy competition within markets.

What are potential drawbacks or limitations of using Upper Confidence Bound algorithms in real-world applications

While Upper Confidence Bound (UCB) algorithms have shown effectiveness in optimizing decision-making processes in various applications, there are potential drawbacks and limitations to consider when using them in real-world settings. One limitation is the assumption of independence between actions taken by players or agents, which may not always hold true in complex environments where interactions are interdependent. Additionally, UCB algorithms require accurate estimation of parameters such as rewards and probabilities, which can be challenging to obtain accurately in practice. Moreover, UCB algorithms may struggle with scalability issues when dealing with large datasets or high-dimensional action spaces.

How might the concept of fair reward allocation impact decision-making processes in competitive environments

The concept of fair reward allocation can significantly impact decision-making processes in competitive environments by influencing player behavior and strategies. In a competitive setting where resources are limited or contested among players, implementing fair reward allocation models can incentivize cooperation over competition. Players may be more inclined to collaborate or coordinate their actions to maximize collective rewards rather than solely focusing on individual gains. This shift towards fairness and cooperation could lead to more sustainable outcomes and foster positive relationships among participants within competitive environments.