Expected Values for Variable Network Games

TL;DR

This paper introduces a framework for analyzing expected wealth and payoff distributions in variable network games, extending classical values like the Myerson and Position Values with new axiomatizations.

Contribution

It develops axiomatizations for the Expected Myerson and Position Values in variable network games, broadening their theoretical foundations.

Findings

Axiomatization of the Expected Myerson Value based on component balance, equal bargaining power, and balanced contributions.

Extension of axiomatization of the Position Value to the Expected Position Value.

Analysis of properties of expected wealth levels in variable network games.

Abstract

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.