The component-wise egalitarian Myerson value for Network Games

TL;DR

This paper introduces a new player allocation rule for network games that balances fairness and individual contribution by combining the Myerson value with equal division, offering a flexible measure of solidarity among players.

Contribution

It proposes the component-wise egalitarian Myerson value, a novel convex combination of existing allocation rules, with axiomatic characterizations and an implementation mechanism.

Findings

Provides three axiomatic characterizations of the new value.

Develops an implementation mechanism under subgame perfect Nash equilibrium.

Balances fairness and marginal contribution in network game allocations.

Abstract

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 player-based 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.