A Complex And Adaptive System Model of a Stylized Delegation Relation...

Following a procedure introduced by Guerrero and Axtell, and Leitner and Behrens, we transform the standard economic model for delegation relationships with hidden-action, which was first described by Holmström, from a closed-form (mathematical) model into an agent-based model, which follows the tradition of complexity economics. With our approach, we deviate from rather "heroic" assumptions, which are typically included in similar models, such as rational and homogeneous agents, and implement a complex system version of the hidden-action problem with two types of agents, namely a supervisor and an employee. We characterize agents by (i) limitations in their cognitive capacity (e.g., in terms of limited processing power and limited memory/storage) and the (ii) availability of information about the environment. However, we endow agents with learning capabilities so that they can learn the missing pieces of information over time (with varying accuracy). In the model, the supervisor delegates a task to the employee and uses an incentive system to control its behavior. While the standard model comes up with an optimal incentive scheme immediately, we observe which incentive system emerges from the complex system over time. 

Our analysis focuses on how close and how fast the solution emerging from the actions and decisions of autonomous agents converges to the solution proposed by the standard model, or if even better solutions can be found, and examine how the agent's limited cognitive capacity affects performance. We investigate whether, and if so, how fast an equilibrium solution (i.e., a stable incentive scheme) emerges from our model. In relatively stable environments, we can nearly reach the optimal solution, i.e., the incentive scheme proposed by the standard hidden-action model. A stable solution, surprisingly, emerges earlier in turbulent environments. We operationalize the variations in environmental turbulence by altering the distribution's standard deviation, which we set relative to the optimal outcome x of the standard hidden-action model (second-best solution in [3]). Further, we can see that it is not the employee's but the supervisor's cognitive capacity, which affects the emergent solution's performance.