Modular Pyramidal Hierarchies and Social Norms. An Agent Based Model

We provide a model of hierarchical organization where artificial agents with limited individual capacities allocate their efforts in two activities. Different incentives schemes are considered and individual diversity and social norms are approached. Introduction The Moral Hazard literature approaches multi-agent relationships in different ways. Among them, the joint production models provide interesting insights in terms of income distribution among the agents. Another relevant aspect has been the comparison between centralized and decentralized structures as far contracting goes. For example, the literature provides conditions under which the situation where all the contracts are proposed by the principal (centralized organization) is superior to a more decentralized one. Following the joint production approach we consider a modular model of hierarchical organization. Specifically, we consider pyramidal structures. This particular structure is spread wise and, consequently, both the economic (see Beckmann, 1988, for a formal analysis) and simulative literature (for instance see Glance and Huberman, 1994) finds interest. For an analysis of the different approaches to pyramidal structures see Merlone (2003). In our model, the organization consists of heterogeneous agents interacting in supervised teams with a Cobb-Douglas production function. We provide a theoretical analysis of the agents interaction in the modular element of the organization. Furthermore, we study the impact of heterogeneity of agents, social norms and incentive schemes in the organization. While in each team there exist infinite solutions to the optimal effort allocation problem, the presence of a social norm allows the selection of one of them. When considering this simple model of supervised team embedded in a multi-layer organization, the complex dynamics between the agents call for the simulation approach. The Agent-Based simulation model we consider allows the extension of the results obtained in the theoretical analysis of the supervised team. First, using the simulation platform we develop, it is possible to consider complex dynamics where agents adapt their efforts to different incentive schemes and to the observable variables. Second, it is possible to study the overall performance of organization when considering different characteristics of the agents, namely managerial capacity, individual capacity, sensitivity to different social norms and rewards. Finally, different adaptive managerial behaviors are compared. Our results shed light on some aspects of interaction between individuals in complex environment and economic performance and give insights in terms of observation of the performance measures in the organization. Furthermore, we prove that, while in general rewards based only on observable efforts by supervisor lead to the underperformance of the organization, under certain circumstances, this kind of rewards allows to an improvement in the performance when a social norm is considered. The model We consider a hierarchical modular model of organization. Each module consists of a supervisor and two subordinates as shown in the following figure. The organization we consider is modular i.e., each supervisor is paired with a same level one and both are in turn supervised by another manager. The organization may consist up to six layers of agents for a total of sixty-three agents. Obviously, the module is the most elementary organization, with only two layers. In the following figure we can see an example of a four layers organization where modules are well recognizable. In the organization, bottom levels individuals are referred as operatives, middle level individuals are referred as managers and the top level individual is referred as the C.E.O. As a consequence, in our hierarchy operatives play only the subordinate’s role, the C.E.O. plays only the supervisor’s role, while managers play both, i.e. they are at the same time supervisors and subordinates. Let us consider a general organization where agents are identified by an index i belonging to the set {0, 1, ..., 62}. Agent i has a capacity ci to be allocated between effort li provided with its partner and effort ui provided with its supervisor. The joint production function for agents 1 and 2 is ( ) ( ) α 2 1 2 1 l l u u + + where 1 < < α 0 and 1 < < β 0 are respectively the output elasticity with respect to the joint effort with the supervisor and with the partner. The following picture illustrates the allocation of the efforts exerted by the two considered agents. We assume that each agent’s capacity is private information. For bottom level agents it remains constant over time while, for the others, it depends on the subordinates output. This is consistent to Quian (1994) where the final output of the hierarchy is determined by a production function which is cumulative in the efforts of workers and managers at all levels. Furthermore, each agent can observe the level effort his/her partners provides but cannot observe the effort his/her partner provides with the boss. By converse, the supervisor can observe the joint output and the effort each agent provides with her. Finally, we assume that each agent knows the average efforts provided with partners and supervisors in his/her level. The agent’s retribution is given by a fixed wage plus a linear incentive proportional to the joint output of the team and a linear incentive on the effort each agent exerts with the supervisor. The net output of the supervised team is the supervisor’s capacity if she is up to work in some other supervised team, or the organization output if she is at the top of the organization. Since, as we said above, a different place in the organization implies a different role, in the following we restrict our analysis to a single module considering the agents’ and the supervisor’s problem.