New Perspectives in Online Contract Design: Heterogeneous, Homogeneous,
  Non-myopic Agents and Team Production
Shiliang Zuo
This work studies the repeated principal-agent problem from an online
learning perspective. The principal's goal is to learn the optimal contract
that maximizes her utility through repeated interactions, without prior
knowledge of the agent's type (i.e., the agent's cost and production
functions).
  I study three different settings when the principal contracts with a
$\textit{single}$ agent each round: 1. The agents are heterogeneous; 2. the
agents are homogenous; 3. the principal interacts with the same agent and the
agent is non-myopic. I present different approaches and techniques for
designing learning algorithms in each setting. For heterogeneous agent types, I
identify a condition that allows the problem to be reduced to Lipschitz bandits
directly. For identical agents, I give a polynomial sample complexity scheme to
learn the optimal contract based on inverse game theory. For strategic
non-myopic agents, I design a low strategic-regret mechanism. Also, I identify
a connection between linear contracts and posted-price auctions, showing the
two can be reduced to one another, and give a regret lower bound on learning
the optimal linear contract based on this observation.
  I also study a $\textit{team production}$ model. I identify a condition under
which the principal's learning problem can be reformulated as solving a family
of convex programs, thereby showing the optimal contract can be found
efficiently.