Static and Repeated Cooperative Games for the Optimization of the AoI in IoT Networks

TL;DR

This paper addresses AoI minimization in a distributed IoT setting with two uncoordinated sensors updating a common server. It develops a static complete-information game with an incentive mechanism and a finite-horizon repeated game, introducing the PoDU metric to compare against a centralized optimum. The authors analytically characterize three pure-strategy Nash equilibria and one mixed equilibrium in the static game and demonstrate via simulations that the repeated game achieves near-optimal AoI in many parameter regimes, with PoDU typically close to 1. The work highlights the viability of decentralized strategies with incentives, and points to extensions to larger sensor networks and partial update correlations as future directions.

Abstract

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.

Figures (7)

• Figure 1:
• Figure 2: Pure and mixed strategy equilibria where at least one player transmits.
• Figure 3: Variation of equilibrium utility with respect to $c_i$.
• Figure 4: Variation of equilibrium utility with respect to $\alpha_i$.
• Figure 5: Utility at equilibrium as a function of $G_1$.