Encouraging the grand coalition in convex cooperative games

TL;DR

This paper investigates solution functions in convex cooperative games that promote the formation of the grand coalition, highlighting the Shapley value's universal encouraging property and the tau-value's limited scope.

Contribution

It demonstrates that the Shapley value always encourages the grand coalition in convex games, while the tau-value does so only for games with up to three players.

Findings

Shapley value encourages the grand coalition in all convex games.

Tau-value encourages the grand coalition in convex games with up to three players.

Encouraging solutions always produce core allocations, but not all core allocations encourage the grand coalition.

Abstract

A solution function for convex transferable utility games encourages the grand coalition if no player prefers (in a precise sense defined in the text) any coalition to the grand coalition. We show that the Shapley value encourages the grand coalition in all convex games and the tau-value encourages the grand coalitions in convex games up to three (but not more than three) players. Solution functions that encourage the grand coalition in convex games always produce allocations in the core, but the converse is not necessarily true.