Equilibrium Analysis of Customer Attraction Games

TL;DR

This paper models competition among online content providers through a customer attraction game, analyzing equilibrium existence, computational complexity, and efficiency bounds in symmetric and asymmetric scenarios.

Contribution

It introduces the customer attraction game model, analyzes equilibrium existence and complexity, and provides approximation schemes and efficiency bounds.

Findings

Pure Nash equilibrium exists in symmetric settings

Finding a PNE is PLS-complete; approximate PNE can be efficiently computed

Existence of PNE is NP-hard in asymmetric settings; approximate PNE exists

Abstract

We introduce a game model called "customer attraction game" to demonstrate the competition among online content providers. In this model, customers exhibit interest in various topics. Each content provider selects one topic and benefits from the attracted customers. We investigate both symmetric and asymmetric settings involving agents and customers. In the symmetric setting, the existence of pure Nash equilibrium (PNE) is guaranteed, but finding a PNE is PLS-complete. To address this, we propose a fully polynomial time approximation scheme to identify an approximate PNE. Moreover, the tight Price of Anarchy (PoA) is established. In the asymmetric setting, we show the nonexistence of PNE in certain instances and establish that determining its existence is NP-hard. Nevertheless, we prove the existence of an approximate PNE. Additionally, when agents select topics sequentially, we demonstrate that finding a subgame-perfect equilibrium is PSPACE-hard. Furthermore, we present the sequential PoA for the two-agent setting.