The Networked Common Goods Game

TL;DR

The paper introduces the networked common goods game (NCGG), analyzing its equilibrium properties, computational complexity, and efficiency loss, revealing both its potential and limitations in networked resource sharing scenarios.

Contribution

It provides the first comprehensive analysis of NCGG, including equilibrium characterization, computational solutions, and efficiency bounds, advancing understanding of networked common goods interactions.

Findings

Single-agent optimization is efficiently solvable.

Pure strategy Nash equilibrium is unique and network-structure dependent.

The game is a potential game with fast convergence to equilibrium.

Abstract

We introduce a new class of games called the networked common goods game (NCGG), which generalizes the well-known common goods game. We focus on a fairly general subclass of the game where each agent's utility functions are the same across all goods the agent is entitled to and satisfy certain natural properties (diminishing return and smoothness). We give a comprehensive set of technical results listed as follows. * We show the optimization problem faced by a single agent can be solved efficiently in this subclass. The discrete version of the problem is however NP-hard but admits an fully polynomial time approximation scheme (FPTAS). * We show uniqueness results of pure strategy Nash equilibrium of NCGG, and that the equilibrium is fully characterized by the structure of the network and independent of the choices and combinations of agent utility functions. * We show NCGG is a potential game, and give an implementation of best/better response Nash dynamics that lead to fast convergence to an $\epsilon$-approximate pure strategy Nash equilibrium. * Lastly, we show the price of anarchy of NCGG can be as large as $\Omega(n^{1-\epsilon})$ (for any $\epsilon>0$), which means selfish behavior in NCGG can lead to extremely inefficient social outcomes.