Price equilibria with positive margins in loyal-strategic markets with discrete prices

TL;DR

This paper investigates how discrete pricing and customer loyalty influence market equilibria in supply chains, revealing multiple equilibria, potential instability, and the impact of price granularity on competition.

Contribution

It introduces a supply chain model with discrete prices and customer loyalty, analyzing equilibrium multiplicity and stability, which were not addressed in continuous pricing models.

Findings

Nash equilibria are not unique in the model.

Low denomination factors can cause game instability.

Small price changes significantly affect market dynamics.

Abstract

In competitive supply chains (SCs), pricing decisions are crucial, as they directly impact market share and profitability. Traditional SC models often assume continuous pricing for mathematical convenience, overlooking the practical reality of discrete price increments driven by currency constraints. Additionally, customer behavior, influenced by loyalty and strategic considerations, plays a significant role in purchasing decisions. To address these gaps, this study examines a SC model involving one supplier and two manufacturers, incorporating realistic factors such as customer demand segmentation and discrete price setting. Our analysis shows that the Nash equilibria (NE) among manufacturers are not unique, we then discuss the focal equilibrium. Our analysis also reveals that low denomination factors can lead to instability as the corresponding game does not have NE. Numerical simulations demonstrate that even small changes in price increments significantly affect the competitive dynamics and market share distribution.