Prospect Theoretic Contract Design in a Stackelberg Game via Bayesian Inference

Abstract

Dynamic contract design with a cognitively biased principal is studied in this work using a Stackelberg game framework. Prospect theory is used to model the decision making of the cognitively biased principal. The goal of the principal is to design a sequence of contracts when faced with adverse selection-lack of knowledge of agent's private information- and moral hazard- noisy observation of agent's effort. The principal observes the noisy output of the agent's effort and using the prior probabilities of the agent's private information, performs a Bayesian inference of the agent's type taking into account Prospect theoretic probability weighting. The prospect theoretic decision making of principal is studied for a static game (one shot) and a dynamic game (finite number of rounds). It is demonstrated that the agent will benefit from principal's irrationality by extracting higher rent than the game with a rational principal. Theoretical results are derived for the binary type games, and the investigation is expanded to an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> -ary hypothesis testing framework through numerical simulation results. The results demonstrate that in estimating the agent's type, a cognitively biased principal becomes more conservative to ensure agent's participation in the game than a rational principal thus allowing increased rent for the agent.