Network Games: The Cooperative Approach

Borkotokey, Surajit; Gogoi, Loyimee; Kumar, Rajnish

doi:10.1007/978-981-13-8319-9_21

Cited by 5 publications

(4 citation statements)

References 48 publications

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“…In this section, we compile the basic notations, definitions, and results from [1,2,3,6,7,11] required for the development of our model. Let N = {1, 2, .…”

Section: Preliminariesmentioning

confidence: 99%

The k-Egalitarian Myerson values: Characterizations and Implementation

Boruah,

Kakoty,

Borkotokey

2024

Preprint

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Network games under cooperative setups have gained significant attention due to their potential applications in various fields, involving humans, computers and society. Players in such games generate values by forming networks under binding agreements. The challenge lies in identifying an appropriate allocation rule that can effectively distribute the generated value. Allocation rules are either player-based or link-based. The Equal Division rule and the Myerson value are two widely used player-based allocation rules, rooted in egalitarian and marginalistic principles, respectively. Egalitarianism emphasizes equality and fairness among individuals, while marginalism focuses on individuals’ additional involvement in a particular work and their inequalities. However, in many real situations, both these mechanisms are inadequate to deal with societal issues as egalitarianism attempts to establish equality, while marginalism highlights existing inequalities. Therefore, a trade-off between these two mechanisms has gained ample interest in recent years. In this paper, we propose a player-based allocation rule for network games that consolidates the Equal Division rule and the Myerson value. The proposed rule allocates an equal share to each player in a component with a size not surpassing a specified number k, and assigns her marginal contributions in components with a size exceeding k. Further, we provide axiomatic characterisations and a bidding mechanism that implements our proposed allocation rule.

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“…In this section, we compile the basic notations, definitions, and results from [1,2,3,6,7,11] required for the development of our model. Let N = {1, 2, .…”

Section: Preliminariesmentioning

confidence: 99%

The k-Egalitarian Myerson values: Characterizations and Implementation

Boruah,

Kakoty,

Borkotokey

2024

Preprint

Self Cite

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“…In this section, we compile the preliminary notations, definitions, and results from [1,2,4,11,16] required for the development of our model.…”

Section: Model Formulationmentioning

confidence: 99%

The component-wise egalitarian Myerson value for Network Games

Borkotokey¹,

Goala²,

Kakoty³

et al. 2022

Preprint

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We introduce the component-wise egalitarian Myerson value for network games. This new value being a convex combination of the Myerson value and the component-wise equal division rule is a playerbased allocation rule. In network games under the cooperative framework, the Myerson value is an extreme example of marginalism, while the equal division rule signifies egalitarianism. In the proposed component-wise egalitarian Myerson value, a convexity parameter combines these two attributes and determines the degree of solidarity to the players. Here, by solidarity, we mean the mutual support or compensation among the players in a network. We provide three axiomatic characterizations of the value. Further, we propose an implementation mechanism for the component-wise egalitarian Myerson value under subgame perfect Nash equilibrium.

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“…An excellent argument for this can be found in von Rueden (2020), where the author comments that since the beginning of the civilization, humans have been mostly living as a species in relatively egalitarian, small-scale societies. The ecological and demographic conditions common to small-scale societies favored the suppression of steep, 1 More recently the network allocation rules (see, e.g., Borkotokey et al, 2019Borkotokey et al, , 2015 have found applications in Bioinformatics (see, e.g., Bora et al, 2020 and the references therein).…”

Section: Introductionmentioning

confidence: 99%

A new value for cooperative games based on coalition size

Borkotokey

Choudhury

Kumar

et al. 2023

Int J of Economic Theory

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We propose and characterize a new value for TU cooperative games based on egalitarian distribution of worths in smaller coalitions and players' marginal productivity in larger coalitions. This value belongs to the class of Procedural values due to Malawski. Our value is identical with the Shapley value on one extreme and the Equal Division rule on the other extreme. We show that our value is identical with the solidarity value due to Bèal et al. of the dual game. However, by duality, our characterization intuitively improves over the axiomatization of this solidarity value. We also provide a mechanism that implements our value in sub‐game perfect Nash equilibrium. Finally, a generalized version of this value is proposed followed by its characterizations.

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Network Games: The Cooperative Approach

Cited by 5 publications

References 48 publications

The k-Egalitarian Myerson values: Characterizations and Implementation

The k-Egalitarian Myerson values: Characterizations and Implementation

The component-wise egalitarian Myerson value for Network Games

A new value for cooperative games based on coalition size

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