Bachelor of Arts
In a principal-agent relationship, the principal offers a take-it-or-leave-it contract to the agent, who decides to either accept it or not. In game theory terminology, the principal agent relationship is a Stackelberg game in which the principal is the leader, proposing the contract, and the agent is the follower, choosing to accept or reject the proposal. Examples of such relationships are plentiful, such as a principal bank manager hiring an agent employee to work as a teller, a principal land-owner acting hiring an agent farmer to grow crops on her land, or an insurance company offering a home insurance plan to a homeowner. The principal-agent problem concerns how the principal should structure the proposed contract to best incentivize the agent to perform in the way the principal would prefer, taking into account that there are informational asymmetries between the principal and the agent due to the agent having some kind of "private information." Information asymmetries between principal and agent fall into two categories: the agent might have private information about their own characteristics, which gives rise to adverse selection problems; or the agent might have private information about what actions he takes after agreeing to the contract, which gives rise to moral hazard problems. In this paper, I focus on a model with moral hazard. The texts by Kreps  and Salanié  both offer good expositions of canonical adverse selection and moral hazard problems, which I used as a starting point for this paper. The survey of different extensions of the principal-agent model by Sappington  provided a high-level guide to different sub-problems and primary sources.
To motivate the model analyzed in this paper, suppose you own several tracts of land that are suitable for agriculture. You want to set up farms on these tracts of land, but you lack the time or expertise to farm the land yourself. You decide, then, to hire several farmers to set up and manage farms on your land. The farmers work year-round and, come harvest time, you pay each of them a sum of money based on their total production. Your challenge is to decide how much money to pay each farmer. Ideally, you would like to be able to pay each worker for the amount of effort that they put in. Unfortunately, you are only able to observe each farmer's output, and there are factors other than the farmer's effort level that affect output. For instance, the amount of rainfall is a random variable that affects all farmers' output equally, but which you are unable to observe. There are also idiosyncratic random variables unique to each farmer that represent the effects of soil condition, pests, and other similar concerns on the tract of land that farmer is working. All else equal, each farmer would prefer to work as little as possible, because they find working displeasurable. As the principal, however, you want the farmers to work as hard as is necessary to maximize your profits. The problem you face is how to structure the farmers' payment scheme so as to align their incentives with your own.
The following analysis will compare individual contracts, in which each agent's payment is based only on the realized magnitude of their output, and tournament payment schemes, in which each agent's payment is based only on the ordinal ranking of their realized output relative to that of all other agents'. Much of the model notation as well as the results from Section 5 are an expanded exposition of results from a paper by Green and Stokey . Lazear and Rosen  provided helpful intuition for the comparison of contracts and tournaments, and some of the results from earlier sections of the paper are due to Grossman and Hart .
Foust, James, "Payment Schemes and Moral Hazard" (2013). Honors Papers. 321.