A Theory of Competitive Sanctions : How to Use the Sticks and the Carrots to Manage Classroom, Workplace, and Society?

In this paper, we provide a theory of positive and negative sanctions using a game theoretic framework. We approach the question of how to use and combine the stick and the carrot policy from the stand that reward is an incentive system for pulling up the good performers and punishment is an incentive for pushing up the bad performers. To investigate the effect of punishment and reward, we introduce a performance selection game (PSG) as the basic framework. On comparing the equilibrium strategy for punishment and that for reward, we find that median ability plays a key role in understanding the characteristics of the performance improving effect of the two incentive schemes. The optimal choice of sanctions is informed by task type as well as degree of heterogeneity of members. We show that punishment is more useful when the task is conjunctive or the group members are homogeneous (member skills, abilities, or tastes are less diverse), and reward is more useful when the task is disjunctive or group members are heterogeneous (member skills, abilities, or tastes are more diverse). We test our results by applying them to the field of education, a workplace, and a society