Game-Theoretic Analysis of Pricing Models in a Dyadic Supply Chain With Fairness Concerns

Introduction

The implicit assumption in the conventional analytical models of supply chain is that the objective of all of its supply chain members is to maximize their own individual profits. However, in the recent years, researchers have found that people are not purely self-interested, and they may exhibit cognitive biases (Appan et al., 2017; Jha & Singh, 2017; Li, 2017) and social preferences, for example fairness concern (Loch & Wu, 2007; D’Rosario, 2017; Sharma & Nandi, 2018; Sarkar & Chakraborty, 2019). There are significant number of cases in which firms, like individuals, are motivated by concerns of fairness (Kahneman et al., 1986). Fairness concern in the context of supply chain management, implies that the firms compare their profits with their counterparts during a supply chain interaction. They feel unfair if they earn either lesser or greater than what they feel is the fair distribution of total pie (Fehr & Schmidt, 1999). In addition, fairness concerns play an important role in motivating and regulating the channel relationships (Rabin, 1993; Geyskens et al., 1998; Fehr & Gächter, 2000). Scheer et al. (2003) show how in comparison to the USA auto dealers, Dutch auto dealers are more averse to gaining more profits than their counterparts. There are also some examples from industry in which the channel relationships between the two supply chain partners in a dyadic supply chain (single buyer-single supplier) were broken because of fairness concerns. For example, the largest instant noodle manufacturer of China, Tingyi Holding Corporation (manufacturer), aborted their transactions with Guangzhou Friendship Group in 2011 (retailer), because Tingyi Holding Corporation one-sidedly raised the wholesale price of noodles, which Guangzhou Friendship Group felt as unfair treatment in the transaction (Li et al., 2018b). In another instance, the Langsha Group, China’s largest socks manufacturer discontinued their business with Wal-Mart in 2007, due to unfair share of benefit allocations (see, e.g., Nie and Du, 2017). In one more example, Xuzhou Wanji Trading of China, an important distributor of Procter & Gamble (P&G) stopped their business with P&G in 2010, due to disproportionate profit shares (see, e.g., Du et al., 2014).

Almost all the current supply chain models that investigate fairness in supply chain coordination (or, buyer-supplier relationship) assume the market as group of oligopolies, where one of the channel members has more bargaining power than its counterpart. The researchers model such games using the Stackelberg game framework, where one player’s decision is based on the response function from other player. For example, if the manufacturer is the dominant player, it will choose its wholesale price, depending on the retailer’s best possible response of its retail price. However, scant evidence has been provided where fairness concerns are investigated in the market scenario where firms possess equal bargaining powers and they make their decisions simultaneously. For example, in small and medium-sized firms, both the manufacturer and the retailer exhibit almost equal bargaining powers. In such situation, none of the players dominate the market over the other and their respective pricing decisions are conditioned on each other’s pricing decision. Thus, to fill this gap, in this paper, we establish a dyadic supply chain model with one manufacturer and one retailer (both are fairness concerned) and investigate their pricing decisions in two non-cooperative game-theoretical frameworks: manufacturer-led Stackelberg game (difference bargaining power), and Vertical Nash game (equal bargaining power)¹. We then derive the equilibrium prices in both the game models and analyze the impact of each channel member’s fairness concern on these prices, with a comparative analysis of prices.

The key objectives of the paper are following: