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Dynamic Incentives

Paper Session

Saturday, Jan. 4, 2020 8:00 AM - 10:00 AM (PDT)

Marriott Marquis, Carlsbad
Hosted By: Econometric Society
  • Chair: Gonzalo Cisternas, Massachusetts Institute of Technology

Optimal Project Management

Alessandro Bonatti
Massachusetts Institute of Technology
Esat Doruk Cetemen
Collegio Carlo Alberto
Juuso Toikka
University of Pennsylvania


We study the optimal incentives provision in long-term projects. The project is successful if and only if the progress level of the project reaches the exogenously specified threshold. Progress of the project is stochastic and proportional to the funds invested in it. Required funding is provided by the principal and the principal requires the agent’s expertise to run the project. The agent can privately divert funds for personal use. We characterize the optimal contract. Optimal contract consists of two regions (efficient and inefficient region) and a path-dependent bonus. If the agent’s continuation utility is high enough principle can implement the first-best policy.

Optimal Contracts with Randomly Arriving Tasks

Daniel Bird
Tel Aviv University
Alex Frug
Pompeu Fabra University


Workers rarely perform exactly the same tasks every day. Instead, their daily work-load may change randomly over time to comply with the fluctuating needs of the organization where they are employed. In this paper, we show that this typical randomness in workplaces has a striking effect on the structure of long-term employment contracts. In particular, simple intertemporal variability in the worker's tasks is sufficient to generate a rich promotion-based dynamics in which, occasionally, the worker receives (a permanent) wage rise and his future work-requirements are reduced.

Optimal Dynamic Contract of Influence

Yi Chen
Cornell University


I study the optimal dynamic contract in a long-term principal-agent relationship, where the agent privately observes an evolving state but his preferences are state-independent. The principal commits to action flows based solely on the agent's reports. I show that communication is generically effective despite the misaligned preferences. Moreover, the optimal contract can stipulate actions that move in the opposite direction of the principal's ideal actions; a necessary and sufficient condition is provided. The principal is worse off over time in expectation, but the agent is not necessarily immiserated. The results apply to dynamic allocation problems such as capital budgeting.

Moral Hazard in Stochastic Differential Games: Beyond Markov Equilibrium

Yuliy Sannikov
Stanford University
Eduardo Faingold
Insper Institute of Education and Research


We study repeated and stochastic games in continuous time with
imperfect public monitoring that have two or more players. We
characterize the full set of public perfect equilibria and attainable
payoffs. For stochastic games, this class of equilibria go beyond
Markov, and the set of attainable payoffs in classic examples can be
significantly larger. We introduce two types of optimality equations
to characterize equilibria: one is elliptic and another, parabolic.
The set of equilibrium payoffs solves the elliptic equation, but it
may not be a unique solution. The parabolic equation has a unique
solution, and we develop a numerical algorithm to find it. Unlike in
two-player repeated games, the optimal equilibria in these games have
new features, such as absorbing regimes which do not correspond to a
static Nash or a Markov equilibrium.

Signaling with Private Monitoring

Gonzalo Cisternas
Massachusetts Institute of Technology
Aaron Kolb
Indiana University


A long-lived player of a normally distributed type interacts with a myopic player over a finite horizon. The myopic player privately observes a noisy signal of the long- lived player’s actions, while the latter can learn about the myopic player’s information from a noisy public signal. Flow payoffs are linear-quadratic, and noise is Brownian. We construct linear-Markov equilibria using the players’ beliefs up to the second order as states. In such equilibria, the long-lived player’s second-order belief is controlled, reflecting that past actions are used to forecast the continuation game. Via this higher- order belief channel, the informational content of the long-lived player’s action is not only driven by the weight attached to her type, but also by how aggressively she has signaled in the past. We investigate the corresponding learning and payoff implications in applications to leadership, political career concerns, and models of insider trading.
JEL Classifications
  • C7 - Game Theory and Bargaining Theory
  • D8 - Information, Knowledge, and Uncertainty