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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

Improving social welfare in non-cooperative games with different types of quantum resources

Résumé

We investigate what quantum advantages can be obtained in multipartite non-cooperative games by studying how different types of quantum resources can improve social welfare, a measure of the quality of a Nash equilibrium. We study how these advantages in quantum social welfare depend on the bias of the game, and improve upon the separation that was previously obtained using pseudo-telepathic strategies. Two different quantum settings are analysed: a first, in which players are given direct access to an entangled quantum state, and a second, which we introduce here, in which they are only given classical advice obtained from quantum devices. For a given game G, these two settings give rise to different equilibria characterised by the sets of equilibrium correlations Qcorr(G) and Q(G), respectively. We show that Q(G) ⊆ Qcorr(G) and, by considering explicit example games and exploiting SDP optimisation methods, provide indications of a strict separation between the social welfare attainable in the two settings. This provides a new angle towards understanding the limits and advantages of delegating quantum measurements.
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Dates et versions

hal-03839608 , version 1 (04-11-2022)

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Alastair A. Abbott, Mehdi Mhalla, Pierre Pocreau. Improving social welfare in non-cooperative games with different types of quantum resources. 2022. ⟨hal-03839608⟩
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