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Quantization Games on Social Networks and Language Evolution

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Document pages: 15 pages

Abstract: We consider a strategic network quantizer design setting where agents mustbalance fidelity in representing their local source distributions against theirability to successfully communicate with other connected agents. We study theproblem as a network game and show existence of Nash equilibrium quantizers.For any agent, under Nash equilibrium, the word representing a given partitionregion is the conditional expectation of the mixture of local and social sourceprobability distributions within the region. Since having knowledge of theoriginal source of information in the network may not be realistic, we showthat under certain conditions, the agents need not know the source origin andyet still settle on a Nash equilibrium using only the observed sources.Further, the network may converge to equilibrium through a distributed versionof the Lloyd-Max algorithm. In contrast to traditional results in the evolutionof language, we find several vocabularies may coexist in the Nash equilibrium,with each individual having exactly one of these vocabularies. The overlapbetween vocabularies is high for individuals that communicate frequently andhave similar local sources. Finally, we argue that error in translation along achain of communication does not grow if and only if the chain consists ofagents with shared vocabulary. Numerical results are given.

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