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Journal of Logic, Language and Information
Erschienen in: Journal of Logic, Language and Information 2/2022

23.03.2022

Who Should Be My Friends? Social Balance from the Perspective of Game Theory

verfasst von: Wiebe van der Hoek, Louwe B. Kuijer, Yì N. Wáng

Erschienen in: Journal of Logic, Language and Information | Ausgabe 2/2022

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Abstract

We define balance games, which describe the formation of friendships and enmity in social networks. We show that if the agents give high priority to future profits over short term gains, all Pareto optimal strategies will eventually result in a balanced network. If, on the other hand, agents prioritize short term gains over the long term, every Nash equilibrium eventually results in a network that is stable but that might not be balanced.
Vorheriger Artikel A Logic for Conditional Local Strategic Reasoning
Nächster Artikel A Modal Logic for Supervised Learning

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Fußnoten
1
Neither of these restrictions is fundamentally necessary, all proofs presented in this paper can easily be adapted to mixed strategies that do use memory. But the restrictions do greatly simplify the proofs, so we assume them for reasons of clarity of presentation.
 
2
The lack of an attitude may be due to an agent’s ignorance or unawareness of the other. Occasionally we may also understand a 0-edge to be a neutral or indifference attitude.
 
3
We consider it hard for someone to go from a positive or negative attitude towards someone to be ignorant of that person, so 00 is in general not a possible output of \({+}{0}\).
 
4
The notion of balance in Harary et al. (1965) is defined for a less general concept, in the sense that our definition of balance in Sect. 5.1 (only for pairs and triads, but not longer cycles) is called 3-balance there, and the balance defined there needs to be achieved for any length of cycles. For details see (Harary et al. 1965, p. 341).
 
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Metadaten
Titel
Who Should Be My Friends? Social Balance from the Perspective of Game Theory
verfasst von
Wiebe van der Hoek
Louwe B. Kuijer
Yì N. Wáng
Publikationsdatum
23.03.2022
Verlag
Springer Netherlands
Erschienen in
Journal of Logic, Language and Information / Ausgabe 2/2022
Print ISSN: 0925-8531
Elektronische ISSN: 1572-9583
DOI
https://doi.org/10.1007/s10849-022-09356-z

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