What level do disadvantaged firms weight rivals' profits in relative performance evaluations under quantity competition?

Abstract

In the context of quantity competition in relative performance evaluation, this study explores the weight placed on rivals' profits through two asymmetry cases—the cost difference between firms and the sequential choice of weight placed on their rivals' profits. We identify high‐cost firms in the cost asymmetry, and followers in the sequential case of weight decisions are labeled “disadvantaged” firms. Whereas the classical literature demonstrates that the weight placed on a rival's profit is negative under quantity competition, we provide theoretical evidence that the disadvantaged firm assigns a positive weight to the rival's profit under asymmetric cases.

Weight assigned to a rival's profit by an advantaged firm in relative performance evaluation with Cournot–Bertrand competition

“…This mechanism is the same as the described by Hamamura (2021b). When the rival decides the quantity, the own decision variable is substituted.…”

“…Based on Hamamura (2021b), we construct our model in this study. We assume the existence of two firms, Firms 1 and 2, which engage in competition in a final goods market.…”

“…This outcome is a consequence of the asymmetric cost assumption. According to Hamamura (2021a, 2021b), then the cost difference has an important effect on the disadvantaged firm strategy.…”

“…In addition, from Equation (), when a < c /(1 − b ) holds, . When both firms decide the quantity, Hamamura (2021b) demonstrates that the disadvantaged firm assigns a positive weight to the rival's profit. By contrast, the present study shows that the disadvantaged firm assigns a positive weight to the rival's profit under Cournot–Bertrand competition.…”

“…Following them, several others have considered managerial incentives and RPE (e.g., Chirco et al, 2011; Fanti et al, 2017; Hattori & Tanaka, 2016; Li et al, 2021; Manasakis et al, 2010; Matsumura et al, 2013; Miller & Pazgal, 2001; 2002; 2005; Philipowski, 2019; Vroom, 2006; Wang, 2020). For example, Hamamura (2021b) examines the strategies of “disadvantaged” firms, which are followers in a sequential game or which have no cost advantage. We also assume cost differences between firms which confront duopoly competition, based on Hamamura (2021b).…”