Essays on Incentives, Justice, and Mechanism Design

Abstract

Chapter 1 develops an axiomatic foundation for the classical problem of paying workers in settings where their actions are not observed by the employer. The latter observes the distribution of workers' abilities, has precise or imprecise information on the level of output, and demands fairness. We first characterize workers' pay thanks to a set of axioms developed under conditions of uncertainty and information asymmetry, assuming the employer is Bayesian. This characterization leads to a closed-form reward rule called the informational Bayesian value (IBV). Then, we analyze worker disappointment under the IBV and find that average disappointment is equal to zero for each worker. This latter result is robust to considering all inputs-based types of disappointment, including ex-post, interim, and ex-ante disappointment. The analysis implies that a worker is never disappointed in the long run when the pay rule utilized in an organization under information asymmetry is fair. Chapter 2 analyzes agents' incentives in a production economy where there are both incomplete information and fairness considerations in the allocation of the economy's surplus. Agents hold private information (type or productivity), with each type profile defining a state of the economy. They choose between remaining inactive and participating in production by selecting from a finite set of available actions. This environment defines a new class of Bayesian economies. I show the existence of a pure-strategy Bayesian Nash equilibrium. Additionally, I uncover conditions that guarantee the efficiency and uniqueness of the equilibrium. Importantly, in the absence of fairness principles, an equilibrium may not exist. The findings are robust to several extensions of the basic model. I develop an application to mechanism design. When incentives are aligned with fairness, I uncover a mechanism that is always Pareto-efficient, and that is incentive-compatible and individually rational under certain conditions. This finding has implications for the design of mechanisms in production economies that are compatible with fairness and efficiency while providing incentives for truthful reporting of private information. Chapter 3 considers the problem of evaluating the utility of participating in organizations that involve multiple interacting agents and are characterized by imperfect information in the sense that agents' types are uncertain ex-ante. We show that this problem admits a unique solution along the lines of expected utility theory, and that this solution is fully characterized by a natural extension of the notions of neutrality to ordinary risk and strategic risk introduced by Roth (1977). In addition, we analyze the implications of Roth's risk neutrality for incentives and equilibrium behaviors. We show the existence of rationalizable organizations, wherein uncertainty over agents' actions arises as an equilibrium play. We develop an application to the firm, showing that, under Roth's risk neutrality, workers' equilibrium behaviors do not depend on whether or not the firm possesses information on individual costs. Our second application is to two-sided assignment markets involving sellers and buyers of indivisible goods. We show that, under Roth's risk neutrality, there exists a pricing mechanism that achieves the expected utility of all agents when the optimal matching is unique, and that only achieves the expected utility of sellers when there is more than one optimal matching.