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.