Working Papers

1. Learning in Relational Contracts with Rumen Kostadinov 

Does symmetric uncertainty about compatibility distort incentives? Do inefficient activities within a firm help mitigate incentive problems in the presence of learning?

Abstract: We study relational contracts between a principal and an agent when they face symmetric uncertainty about the match quality. Actions affect learning about the match quality and the principal’s payoffs. Because the agent’s actions are perfectly observable, the agent cannot bias the principal’s beliefs. We show that even when the agent is not protected by limited liability and despite the absence of private information and hidden action, uncertainty about match quality precludes efficiency. The source of inefficiency is the holdup problem arising out of the separation between the entity exerting effort and the entity collecting the output. We characterize the set of all subgame perfect equilibria of the associated game. We show that the Pareto Optimal equilibria may involve actions that are dominated in their informational content as well as payoff. Such actions are a modest way for the principal to provide incentives and learn about the match quality, when more efficient ways are not credible. Conditional upon strong performance, we show that the relationships move to a phase where actions that offer better learning and higher payoff are used. In this phase the agent is rewarded with a bonus upon strong performance.

2. Job Insecurity with Elliot Lipnowski

What is the relationship between job security and productivity, when the risk of firing is endogenously determined?

Abstract: This paper examines the effect of job insecurity on productivity. We study a fixed wage relationship between a firm and a worker in which neither knows how well-suited the worker is to the job. The worker decides the level of effort, a choice that affects both learning and the firm’s bottom line. The employer, seeing the worker’s effort choice and outcome, decides whether or not to continue employing the worker. The employer cannot commit to retain the worker when she becomes pessimistic enough about the match quality. We show that, rather than aligning interests, this threat creates a perverse incentive not to attract attention: the worker strategically slows learning, harming productivity. As the firm anticipates this, job insecurity can be a self-fulfilling prophecy. We explicitly characterize the unique Markov perfect equilibrium in our continuous time dynamic game. Consistent with empirical evidence in organizational psychology, equilibrium exhibits a U-shaped relationship between job insecurity and productivity: a worker is least productive when his job is moderately secure.

3. A Fair Algorithm in a Marriage Market 

We know that the Deferred Acceptance Algorithm (DAA) treats one side of the market favorably. Can we devise a procedure similar to DAA that avoids this favoritism?

Abstract: The celebrated Deferred Acceptance Algorithm (DAA) due to Gale & Shapley always produces an extremal matching by favoring one side of the market at the expense of the other. This favoritism arises because, in DAA, only one side makes proposals. I propose a new algorithm wherein both sides of the market propose in a manner similar to the DAA. The proposed algorithm always yields a stable matching. Moreover, the outcome is often a non-extremal matching. Additionally, the algorithm does not distinguish (ex-ante) between men and women at any stage. The ex-post distinction arises primarily because in every round potential cycles are formed, that are broken arbitrarily. Lastly, the algorithm can be computed in polynomial time and hence, from a practical standpoint, can be used in markets where fairness considerations are important.

Work in Progress 

4. Collaborative Culture with Elliot Lipnowski

How should a firm optimally resolve the tradeoff between fostering collaboration and adapting its decision efficiently to the new information?

Abstract: We study optimal project selection by a firm that must choose between different workers’ preferred projects. The firm faces a basic tradeoff between fostering collaboration among its employees and efficiently adapting its decisions to its circumstances. If the firm commits to choosing the project which is most profitable ex-post, it undermines its employees’ motive to collaborate, causing ex-ante inefficiency. We solve for the firm’s optimal policy. It entails an early phase of intense competition, followed by a permanent regime of efficient collaboration. In service to ex-ante optimality, arbitrarily severe ex-post inefficiencies must be tolerated.

5. Matching with Incomplete Preferences

In a one-sided or two-sided market design framework what is the right notion of stability when the agents have incomplete preferences? How do we obtain a “stable” matching in this environment?