Implications of a relative evaluation in a competitive environment

Abstract

We consider a game-theoretical model in which players’ performances are evaluated in a relative system. Every player simultaneously and independently chooses their effort levels, and the distribution of a player’s performance is determined by the profile of the players’ effort levels. We present the existence of the unique equilibrium of the game, and investigate the properties of the equilibrium. One interesting feature of our model is that a player’s response to a change in other players’ costs depends on whether the player has a lower cost or a large cost. Our model shows that a player with a small cost works harder, whereas a player with a large cost works less, when other players become better. In words, a good player is motivated to work hard, whereas a bad player is discouraged from working hard. This feature implies that a careful consideration should be given when designing a policy concerning supporting students and university. Supporting productive students may be socially desirable since they work harder, but that can discourage other students, which may be less desired. Supporting students with low productivities can reduce the gap between them and productive students. However, the gain in the social welfare due to the supports may not be very big. Another interesting feature of our model is quasi-competitiveness. Our results imply that the quasi-competitiveness may hold in a larger class of oligopoly models rather than the classes usually considered in the existing literature.