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Dynamic Games and Applications

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01.12.2016

The Subgame-Consistent Shapley Value for Dynamic Network Games with Shock

verfasst von: Leon Petrosyan, Artem Sedakov

Erschienen in: Dynamic Games and Applications | Ausgabe 4/2016

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Abstract

In the paper, cooperative repeated network games containing network formation stages are studied. After the first network formation stage, a particular player with a given probability may stop influencing other players by removing all her links and receiving zero payoffs. This effect is called “shock.” The effect of shock may appear only once, and the stage number, at which shock appears, is chosen at random. In the cooperative scenario of the game, subgame consistency of the Shapley value, based on a characteristic function, which is constructed in a special way, is investigated. To prevent players from breaking the cooperative agreement, a mechanism of stage payments—so-called imputation distribution procedure—is designed.

Vorheriger Artikel Network Characteristics Enabling Efficient Coordination: A Simulation Study

Nächster Artikel Mean-Field Game Approach to Admission Control of an M/M/ Queue with Shared Service Cost

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Henceforth, to avoid confusion and simplify understanding, we will not add network formation stages to the number of stages in the game, whereas we will enumerate other stages from 1 to \(\ell \). The game will be considered as an \(\ell \)-stage dynamic game with at most two network formation stages.

It means that starting this moment, all links involving player m are eliminated from the network. However, player m still belongs to set N, but receives zero stage payoffs.

Behavior \((0,{\bar{{\bar{u}}}}_m)\) of player m, who leaves the game after shock, prescribes her to choose control \({\bar{{\bar{u}}}}_m\). However, according to (9), her payoff will be equal to 0 afterward for any of her controls \({\bar{{\bar{u}}}}_m \in U_m\).

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Titel: The Subgame-Consistent Shapley Value for Dynamic Network Games with Shock
verfasst von: Leon Petrosyan
Artem Sedakov
Publikationsdatum: 01.12.2016
Verlag: Springer US
Erschienen in: Dynamic Games and Applications / Ausgabe 4/2016
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI: https://doi.org/10.1007/s13235-015-0166-y

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