Product Assortment Games Under Multinomial Logit Model With Endogenous Network Effects

ABSTRACT This paper focuses on assortment competition problems where customers' purchase decisions are modeled using a multinomial logit choice model incorporating endogenous network effects. For non‐negative network effects, we introduce pseudo‐revenue‐ordered assortments to solve the best response problem. For negative network effects, where the pseudo‐revenue‐ordered policy is inapplicable, we propose an efficient implicit enumeration algorithm. We show that, under mild conditions, pure‐strategy Nash equilibria exist in assortment competition games, even with both common and exclusive products. Moreover, such equilibria can be computed in polynomial time under non‐negative network effects. Furthermore, we identify a Pareto‐dominant pure‐strategy Nash equilibrium and provide necessary and sufficient conditions for equilibrium uniqueness. Under cardinality constraints, we prove that games with only exclusive products always have a pure‐strategy Nash equilibrium, though such existence may fail to hold in more general cases. We also study cooperation among retailers and investigate the situations under which stable coalitions emerge in various settings. Our findings suggest that greater positive network effects lead to narrower assortments and increased equilibrium payoffs for all retailers, potentially fostering the blockbuster phenomenon . In contrast, stronger negative network effects drive broader assortments and decreased payoffs, potentially leading to a long tail . Thus, considering network effects in assortment decisions is crucial to avoid suboptimal payoffs, especially in competitive environments.