Quantization Games on Social Networks and Language Evolution

Ankur Mani, Lav R. Varshney, Alex Pentland

Research output: Contribution to journalArticlepeer-review

Abstract

Motivated by collaboration in human and human-robot groups, we consider designing lossy source codes for agents in networks that are in different statistical environments but also must communicate with one another along network connections. This yields a strategic network quantizer design problem where agents must balance fidelity in representing their local source distributions against their ability to successfully communicate with other connected agents. Using network game theory, we show existence of Bayes Nash equilibrium quantizers. For any agent, under Bayes Nash equilibrium, we prove that the word representing a given partition region is the conditional expectation of the mixture of local and social source probability distributions within the region. Since having knowledge of the original source of information in the network may not be realistic, we further prove that under certain conditions, the agents need not know the source origin and yet still settle on a Bayes Nash equilibrium using only the observed sources. Further, we prove the network may converge to equilibrium through a distributed version of the Lloyd-Max algorithm, rather than centralized design. In contrast to traditional results in language evolution, we demonstrate several vocabularies may coexist in Bayes Nash equilibrium, with each individual having exactly one of these vocabularies. The overlap between vocabularies is high for individuals that communicate frequently and have similar local sources. Finally, we prove that error in translation along a chain of communication does not grow if and only if the chain consists of agents with shared vocabulary. Numerical examples demonstrate our findings.

Original languageEnglish (US)
Article number9460761
Pages (from-to)3922-3934
Number of pages13
JournalIEEE Transactions on Signal Processing
Volume69
DOIs
StatePublished - 2021

Bibliographical note

Funding Information:
Manuscript received June 1, 2020; revised December 31, 2020, March 2, 2021, and May 3, 2021; accepted June 1, 2021. Date of publication June 18, 2021; date of current version July 27, 2021. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Hsiao-Chun Wu. This work was supported in part by the National Science Foundation under grant CCF-1717530, and in part by the University of Minnesota Digital Technology Initiative Seed Grant. (Corresponding author: Lav Varshney.) Ankur Mani is with the Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail: amani@umn.edu).

Publisher Copyright:
© 1991-2012 IEEE.

Keywords

  • Game theory
  • language evolution
  • quantization theory
  • social networks

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