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

Abstract

This study examines the weight placed on a rival's profit under asymmetric cost and Cournot–Bertrand competition. From our model analysis, when an advantaged firm decides quantity and a disadvantaged firm decides a price, we find the case where each firm set positive weight placed on a rival's profit. Our result suggests that decision variables in a product market are important to consider CEOs' implicit compensation contract in empirical research. In addition, it is interesting to demonstrate the advantaged firm sets positive weight placed on a rival's profit under quantity decision.

Relative performance evaluation and wage inequality

“…Other forms of utility functions can be adopted. Second, in our model, firms in the product market compete à la Cournot, while there also exists other forms of competition, such as Bertrand competition and Stackelberg competition that have been considered in some researches on RPE (see Aggarwal & Samwick, 1999; Hamamura, 2022; Han et al., 2022). Third, we treat the strength of RPE as an exogenous policy variable.…”

“…They reach to the same conclusion that the optimal weight assigned to the competitors' performance should be positive for strategic complements but negative for strategic substitutes. Following studies expand this topic by considering various cases, such as asymmetric competition (Pal, 2015) and asymmetric cost (Hamamura, 2021(Hamamura, , 2022, and thus enrich the findings. Another strand of literature starts to explore the equilibrium consequences of adopting RPE in various markets.…”

The welfare effect of release timing of relative performance evaluation under quantity competition and asymmetric costs

“…Without loss of generality, we specify that Firm 1 is an advantaged firm and Firm 2 is a disadvantaged firm (i.e., ). Several studies have assumed asymmetric marginal costs among competing firms under the RPE (Hamamura, 2021a, 2021c, 2022; Miller & Pazgal, 2001, 2002). We normalize and for simplicity.…”

Social performance versus relative performance evaluation, asymmetric costs, and quantity competition under managerial delegation

“…Our study also demonstrates that a disadvantaged firm aims to commit to a less aggressive strategy in a product market, and we show that under asymmetric performance measures, the social performance firm sets a negative weight on the performance indicator. Additionally, Hamamura (2021a) considers the disclosure strategy of the performance indicator, and Hamamura (2022) assumes asymmetric competition (i.e., Cournot–Bertrand competition). Recently, Xu and Matsumura (2022) considers an asymmetric performance evaluation system.…”

“…Following Aggarwal and Samwick (1999) and Fumas (1992), several studies consider the impact of RPEs on firm strategies based on the managerial delegation game (e.g., Asseburg & Hofmann, 2010;Chirco et al, 2011;Hattori & Tanaka, 2016;Huang et al, 2020;Matsumura et al, 2013;Miller & Pazgal, 2005;Satoh & Tanaka, 2014;Tanaka, 2014;Xu & Matsumura, 2022). In particular, several studies assume asymmetric marginal costs among competing firms (Hamamura, 2021a(Hamamura, , 2021b(Hamamura, , 2022 and focus on the weight placed on the rival's profit. For example, Miller and Pazgal (2001) considers complementary goods under quantity competition and demonstrates a case in which both firms set positive weights on their rivals' profits.…”