The Power Allocation Game on A Network: A Paradox

TL;DR

This paper uncovers a paradox in a network-based power allocation game where increasing alliances can reduce a country's welfare at equilibrium, challenging intuitive assumptions about cooperation.

Contribution

It introduces a novel paradox in a distributed resource allocation game, showing that more alliances can harm a country's welfare, with conditions and efficiency bounds analyzed.

Findings

Additional friends can decrease a country's welfare in equilibrium.

Conditions for the paradox to occur are derived.

Price of anarchy results are provided.

Abstract

The well-known Braess paradox in congestion games states that adding an additional road to a transportation network may increase the total travel time, and consequently decrease the overall efficiency. Motivated by this, this paper presents a paradox in a similar spirit emerging from another distributed resource allocation game on networks, namely the power allocation game between countries developed in \cite{allocation}. The paradox is that by having additional friends may actually decrease a country's total welfare in equilibrium. Conditions for this paradox to occur as well as some price of anarchy results are also derived.