Wireless sensing and the internet of things (IoT) are nowadays pervasive in 5G and beyond networks, and they are expected to play a crucial role in 6G. However, a centralized optimization of a distributed system is not always possible and cost-efficient. In this paper, we analyze a setting in which two sensors collaboratively update a common server seeking to minimize the age of information (AoI) of the latest sample of a common physical process. We consider a distributed and uncoordinated setting where each sensor lacks information about whether the other decides to update the server. This strategic setting is modeled through game theory (GT) and two games are defined: i) a static game of complete information with an incentive mechanism for cooperation, and ii) a repeated game over a finite horizon where the static game is played at each stage. We perform a mathematical analysis of the static game finding three Nash Equilibria (NEs) in pure strategies and one in mixed strategies. A numerical simulation of the repeated game is also presented and novel and valuable insight into the setting is given thanks to the definition of a new metric, the price of delayed updates (PoDU), which shows that the decentralized solution provides results close to the centralized optimum.

翻译：无线传感与物联网技术如今已广泛渗透至5G及未来网络，并预期将在6G中发挥关键作用。然而，分布式系统的集中式优化并非总是可行且成本高效的。本文研究了一种场景：两个传感器协作更新公共服务器，旨在最小化公共物理过程最新样本的信息年龄。我们考虑一种分布式且非协调的场景，其中每个传感器无法获知对方是否决定更新服务器。该策略场景通过博弈论建模，并定义了两类博弈：i) 具有合作激励机制的完全信息静态博弈；ii) 有限时域上的重复博弈，其中每个阶段进行静态博弈。我们对静态博弈进行了数学分析，发现了三个纯策略纳什均衡和一个混合策略纳什均衡。同时通过数值模拟展示了重复博弈的行为，并借助新定义的指标——延迟更新代价，为该场景提供了新颖且有价值的见解，表明去中心化解决方案能够获得接近集中式最优的结果。