Admission Control for Games with a Dynamic Set of Players

Ilai Bistritz*, Nicholas Bambos

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We consider open games where players arrive according to a Poisson process with rate λ and stay in the game for an exponential random duration with rate μ. The game evolves in continuous time where each player n sets an exponential random clock and updates her action an ∈ {0,⋯, K} when it expires. The players take independent best-response actions that, uninterrupted, can converge to a Nash Equilibrium (NE). This models open multiagent systems such as wireless networks, cloud computing, and online marketplaces. When λ is small, the game spends most of the time in a (time-varying) equilibrium. This equilibrium exhibits predictable behavior and can have performance guarantees by design. However, when λ is too small, the system is under-utilized since not many players are in the game on average. Choosing the maximal λ that the game can support while still spending a target fraction 0 < ρ < 1 of the time at equilibrium requires knowing the reward functions. To overcome that, we propose an online learning algorithm that the gamekeeper uses to adjust the probability θ to admit an incoming player. The gamekeeper only observes whether an action was changed, without observing the action or who played it. We prove that our algorithm learns, with probability 1, a θ∗ such that the game is at equilibrium for at least ρ fraction of the time, and no more than ρ+ϵ(μ,ρ) < 1, where we provide an analytic expression for ϵ(μ,ρ). Our algorithm is a black-box method to transfer performance guarantees of distributed protocols from closed systems to open systems.

Original languageEnglish
Title of host publication2023 62nd IEEE Conference on Decision and Control, CDC 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1219-1224
Number of pages6
ISBN (Electronic)9798350301243
DOIs
StatePublished - 2023
Event62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore
Duration: 13 Dec 202315 Dec 2023

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference62nd IEEE Conference on Decision and Control, CDC 2023
Country/TerritorySingapore
CitySingapore
Period13/12/2315/12/23

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