Optimal Advertisement Spending in a Duopoly with Incomplete Information

Optimal Advertisement Spending in a Duopoly with Incomplete Information

Luis E. Castro (Department of Industrial Engineering, University of Miami, Coral Gables, USA) and Nazrul I. Shaikh (Department of Industrial Engineering, University of Miami, Coral Gables, USA)
Copyright: © 2018 |Pages: 21
DOI: 10.4018/IJBAN.2018070101

Abstract

This article presents the relationship between a firm's advertisement spending and sales in a duopoly when information about the competitors' advertisement spending is unavailable. The competitive interaction between the firms has been modeled as imperfect information Cournot and Stackelberg games and the conditions for subgame perfect Bayesian Nash equilibrium are presented. The results suggest that when the firms are similar in size and advertisement effectiveness, both firms are better off sharing their advertising plans with each other. On the other hand, when one of the firms is a market leader, the follower may profit from the leader's advertisement spending and so is better off keeping the leader guessing. A practical approach to estimate the optimum advertisement budget based on the expected values of the competitors' historic advertising spending is presented as well.
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1. Introduction

Firms often use advertisement to inform potential consumers about their products and features and to differentiate themselves from competitors. Such a tactic is a preferred means of competing in a duopoly as it leads to brand building and category growth while activities such as pricing and merchandising usually lead to the erosion of brand equity and potential price wars (Tellis, 2003; Tirole, 1988). However, determining the optimum advertisement budget is important as both low and high investments impact the firm’s profitability. Prior research has established that factors such as the base demand for the products, the firm’s production levels, the sensitivity of the demand to advertisements, and the competitor’s strategies influence the utility of advertisement for a firm (Chakravarti and Janiszewski, 2004; Mohanty, Clements, & Gupta 2018; Sethuraman, Tellis, & Briesch, 2011; Vakratsas & Ambler, 1999), and all these elements need to be considered in developing a firm’s advertisement strategy.

A vast body of literature discusses the optimal advertisement spending strategies for firms under different conditions (Bass, Krishnamoorthy, Prasad, & Sethi, 2005; Chintagunta & Vilcassim, 1992; Eliashberg & Chatterjee, 1985; Jørgensen & Zaccour, 2014; Paetz, 2017; Sasieni, 1989; Sethi, 1977). The literature on game theory-based approaches generally focus on the role that advertisements plays in influencing the equilibrium when multiple firms are competing or collaborating. Research analyzing the “vertically integrated” firms focuses on the role of advertisement in coordinating retailers and suppliers (Aust and Buscher, 2014a) while the research analyzing the “horizontal” competition focuses on competition and market share dynamics within a product category (Alston, Freebairn, & James, 2001). Researchers, especially from the field of agriculture economics have also looked at the role of collaborative advertisements for competing firms (Alston, Freebairn, & James, 2001). However, these models typically assume that perfect information about the competitors’ strategies is available (Aust & Buscher, 2014a, 2014b; Bonatti, Cisternas, & Toikka, 2017). The reality, especially in the horizontal competitive structure, is that a firm is usually unaware of the competitor’s plans while deciding what its future advertisement spending should be. Further, a firm is typically unaware of the competitor’s products costs as well. They are thus faced with incomplete information.

The present study focuses on the horizontal competition between two firms in a duopoly, producing a substitutable good with no information available for the competitor’s future advertisement spending or product costs. Two models of competition—the Cournot, and the Stackelberg models—have been used to capture the different competitive scenarios between firms. We assume incomplete information and derive insights into a firms’ optimal advertisement spending strategies. The models answer questions such as what a firm’s optimal advertisement spending should be, if a firm has any incentive to play the role of a leader in a duopoly, and if information sharing can arise as a solution to the advertisement spending problem.

The paper is organized as follows. The second section outlines the main literature references on game theory models with advertisement spending. The third section presents the proposed game theoretic formulations for a duopoly using our proposed per-unit cost formulation for advertisement spending. The necessary conditions for the existence of Bayesian Nash Equilibriums (BNE) for the Cournot and the Stackelberg models under incomplete information are also derived. The fourth section builds on the BNE solutions to provide a practical approach to making decisions about advertisement spend and production level when faced with imperfect information about the competitors. The main conclusions and future applied work based on the model is presented in the final section.

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