Mean Field Model for an Advertising Competition in a Duopoly

TL;DR

This paper models advertising competition in a duopoly using mean field game theory, analyzing Nash and Stackelberg-like equilibria to understand strategic advertising behaviors.

Contribution

It introduces a mean field framework for duopoly advertising competition, comparing Nash and multi-leader-follower equilibria, which is a novel approach.

Findings

Different equilibrium concepts lead to distinct strategic insights.

Major players' policies depend on minor players' rationality assumptions.

The model highlights the impact of rationality assumptions on competition outcomes.

Abstract

In this study, we analyze an advertising competition in a duopoly. We consider two different notions of equilibrium. We model the companies in the duopoly as major players, and the consumers as minor players. In our first game model we identify Nash Equilibria (NE) between all the players. Next we frame the model to lead to the search for Multi-Leader-Follower Nash Equilibria (MLF-NE). This approach is reminiscent of Stackelberg games in the sense that the major players design their advertisement policies assuming that the minor players are rational and settle in a Nash Equilibrium among themselves. This rationality assumption reduces the competition between the major players to a 2-player game. After solving these two models for the notions of equilibrium, we analyze the similarities and differences of the two different sets of equilibria.