Maximizing Social Welfare in Score-Based Social Distance Games

TL;DR

This paper introduces a flexible score-based utility framework for social distance games and proves the tractability of finding welfare-maximizing coalitions on tree networks, extending to stability concepts.

Contribution

It establishes the computational feasibility of welfare maximization in score-based social distance games on tree networks for various utility functions.

Findings

Welfare-maximizing coalition partitioning is tractable on tree networks.

Efficient algorithms are provided for specific utility functions and network types.

Results extend to Nash stability and individual rationality conditions.

Abstract

Social distance games have been extensively studied as a coalition formation model where the utilities of agents in each coalition were captured using a utility function u that took into account distances in a given social network. In this paper, we consider a non-normalized score-based definition of social distance games where the utility function u_v depends on a generic scoring vector v, which may be customized to match the specifics of each individual application scenario. As our main technical contribution, we establish the tractability of computing a welfare-maximizing partitioning of the agents into coalitions on tree-like networks, for every score-based function u_v. We provide more efficient algorithms when dealing with specific choices of u_v or simpler networks, and also extend all of these results to computing coalitions that are Nash stable or individually rational. We view these results as a further strong indication of the usefulness of the proposed score-based utility function: even on very simple networks, the problem of computing a welfare-maximizing partitioning into coalitions remains open for the originally considered canonical function u.