Probabilistic network values

TL;DR: In this article, the authors investigated 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 games.

TL;DR: This study investigates expected wealth levels and individual payoffs in variable network games, establishing axiomatizations for the Expected Myerson Value and Expected Position Value based on properties such as component balance and balanced contributions.

TL;DR: A novel profit allocation rule for complex product development networks based on the Position value is presented. The research investigates the relationship between firms' investments and their allocated profits, considering the disconnectedness of development networks. The findings indicate that the network position, investment, and various factors influence firms' profits, with the Position value being more suitable than the Myerson value for complex product development networks.

TL;DR: In this article, the authors study the stability and efficiency of social and economic networks when self-interested individuals can form or sever links, and show that there does not always exist a stable network that is efficient.

TL;DR: Graph-theoretic ideas are used to analyze cooperation structures in games, and fair allocation rules are proven to be unique, closely related to the Shapley value, and stable for a wide class of games.

TL;DR: The multilinear extension of an n-person game v is a function defined on the n-cube IN which is linear in each variable and which coincides with v at the conrners of the cube, satisfying fx = v{i ∣.

TL;DR: An axiomatic characterization of the position value is provided and relations with the Myerson value are discussed, and, for special classes of communication situations, elegant calculation methods for their position values are described.