See https://homepage.ntu.edu.tw/~josephw/MiniCourse_Mult-Agent%20Contracting.pdf

This mini-course on multi-agent contracting will survey some of the recent theoretical literature on incentive schemes in multi-agent environments, with special emphasis on teams and the role peer effects in team- contracting. While most of the course builds on theory papers we will also discuss experimental and empirical papers on team behavior and on peer effects in teams.

We shall start with a short introduction to standard models of principal-multiagent, and then move on to a moral hazard model of organizations in which agents’ effort decisions are mapped into a probability of the project’s success. We shall see that optimal incentive mechanisms may require that agents be rewarded differentially even when they are completely identical and induced to act the same. We shall characterize the environments in which such discrimination is unavoidable in terms of the organizational technology.

Our next step in the course will be to consider models in which agents are asymmetrically informed about each other’s effort. We will start with a model in which agents move sequentially in performing their tasks (as in an assembly line) with each agent observing the effort of his predecessors. We shall see how agents’ role in the production process affects the rewards they receive in the optimal mechanism. We shall use an extended version of the model to address the issue of the optimal allocation of agents and tasks to different production slots depending on agents’ skills and the criticality of tasks to the success of the entire project. In interpreting these results we shall reflect on issues such as the role of leadership and of hierarchies in organizations.

From the model of sequential production, we shall move on to a general model of information among peers, to discuss the role of transparency in organizations. We shall describe information structures among peers by means directed graphs in which an arrow from agent i to agent j represents a situation in which i sees the effort decision of j before making his own decision. We shall discuss conditions under which the cost of providing incentives is declining with the level of transparency in the organization. This model also will allow us to compare architectures of information structures and address several issues on the optimal design of the work area. In particular, we shall show why process-based teams (in which each agent resumes a different function in the production of the same product) are more effective than function-based teams (where all agents perform the same function).

We shall discuss other multi-agent models related to the above models including one in which agents are assumed to interact repeatedly in performing a joint project, and another model in which agents compete under a scheme that rewards them based on relative performance. Within the latter model we shall also demonstrate why excessive monitoring by the principal may be counterproductive even when monitoring is not costly. Next, we shall the anomaly of “incentive reversal.” i.e. situations in which higher rewards are counter-effective. As we shall see in a multi-agent framework such a phenomenon can arise in a fully rational environment (without relying on any behavioral or psychological effect). Finally, will also study several important applications of multi-agent contracting. One such application involves the raising of capital by a firm. We will study the implications of optimal contracting on the choice of investment contracts as well as on the choice of the set of investors. We will also study the role of multi-agent contracting in tort law and explain why such contracts tend to induce excessive care against damages.

While the main part of the course involves theoretical result we will survey a number of experimental and empirical results (based on field data) on incentives and team production. These studies will address the following issues:
1. The role of psychological peer effect and peer pressure in inducing agents to exert effort.
2. Coordination and mis-coordination of efforts in teams.
3. Inter-group solidarity and intra-group conflict.