Probabilistic network values

Borkotokey, Surajit; Chakrabarti, Subhadip; Gilles, Robert P.; Gogoi, Loyimee; Kumar, Rajnish

doi:10.1016/j.mathsocsci.2021.07.003

Cited by 2 publications

(7 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The extent of a network formation probability distribution is recognised as the network that consists of all links that form with positive probabilities, extending the definition of the support developed in Borkotokey et al (2021) for probabilistic networks to the class P N . The components and isolated players in the extent of a network formation probability distribution ρ critically determine the main features of those networks that can emerge under ρ.…”

Section: Network Formation Probability Distributionsmentioning

confidence: 99%

“…Calvo et al (1999) only considered the case of q = 1 in their motivating discussion. Example 2.3 discusses the special case of network formation being based on the independent formation of the individual links that make up the network-further explored in Calvo et al (1999) and Borkotokey et al (2021). In particular, let p : g N → [0, 1] be some assignment of link formation probabilities on g N .…”

Section: A Motivating Example: Intermediated Bilateral Tradementioning

confidence: 99%

“…Calvo et al (1999) extend the Myerson Value to the class of these probabilistic communication situations. Borkotokey et al (2021) extend the probabilistic perspective on link formation of Calvo et al (1999) to the realm of network games. This results in probabilistic network games, where networks are formed stochastically independently based on given link formation probabilities.…”

Section: Introductionmentioning

confidence: 99%

“…This results in probabilistic network games, where networks are formed stochastically independently based on given link formation probabilities. Borkotokey et al (2021) extend and characterize the Myerson Value as well as the Position Value to this framework of probabilistic network games.…”

Section: Introductionmentioning

confidence: 99%

“…It can be argued that the independence hypothesis of link formation is questionable. In their paper, Borkotokey et al (2021) give a practical example of probabilistic network games over the airline code sharing networks. Passengers travelling on intercontinental flights often using multiple airlines who have code sharing agreements with one another.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Expected values for variable network games

Chakrabarti,

Gogoi,

Gilles

et al. 2023

Ann Oper Res

Self Cite

View full text Add to dashboard Cite

A network game assigns a level of collectively generated wealth to every network that can form on a given set of players. A variable network game combines a network game with a network formation probability distribution, describing certain restrictions on network formation. Expected levels of collectively generated wealth and expected individual payoffs can be formulated in this setting. We investigate properties of the resulting expected wealth levels as well as the expected variants of well-established network game values as allocation rules that assign to every variable network game a payoff to the players in a variable network game. We establish two axiomatizations of the Expected Myerson Value, originally formulated and proven on the class of communication situations, based on the well-established component balance, equal bargaining power and balanced contributions properties. Furthermore, we extend an established axiomatization of the Position Value based on the balanced link contribution property to the Expected Position Value.

show abstract

Section: Network Formation Probability Distributionsmentioning

confidence: 99%

Section: A Motivating Example: Intermediated Bilateral Tradementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Expected values for variable network games

Chakrabarti,

Gogoi,

Gilles

et al. 2023

Ann Oper Res

Self Cite

View full text Add to dashboard Cite

show abstract

A novel profit allocation rule of complex product development networks under the position value

Zhang,

Yang,

Zhu

et al. 2024

RAIRO-Oper. Res.

View full text Add to dashboard Cite

A fair and reasonable profit allocation mechanism is the key to ensuring the stability of complex product development networks. Considering the disconnectedness of development networks, this paper takes the Position value to allocate profits. Initially, this paper constructs the profit function of complex product development networks, which serves as the characteristic function in graph cooperative games. Subsequently, a real-world case is presented to demonstrate the profit allocation process using the Position value, allowing for an examination of the relationship between profits and firms' investments. Moreover, various factors are investigated to assess their influence on the profit allocation result, and a comparison is made between the Position value and the Myerson value. By adjusting the parameters and observing the numerical simulation, the research delves into the impact of key parameters on firms' profit allocation. The findings indicate that the network position and investment are directly proportional to firms' allocated profits. Additionally, the synergistic coefficient and benefit coefficient positively moderate firms' profits, while the cost coefficient of investment negatively moderates them. Notably, the Position value proves to be more suitable for complex product development networks than the Myerson value.

show abstract

Probabilistic network values

Cited by 2 publications

References 17 publications

Expected values for variable network games

Expected values for variable network games

A novel profit allocation rule of complex product development networks under the position value

Contact Info

Product

Resources

About