Learning to Mitigate Externalities: the Coase Theorem with Hindsight Rationality

In economic theory, the concept of externality refers to any indirect effect resulting from an interaction between players that affects the social welfare. Most of the models within which externality has been studied assume that agents have perfect knowledge of their environment and preferences. This is a major hindrance to the practical implementation of many proposed solutions. To address this issue, we consider a two-player bandit setting where the actions of one of the players affect the other player and we extend the Coase theorem [Coase, 1960]. This result shows that the optimal approach for maximizing the social welfare in the presence of externality is to establish property rights, i.e., enable transfers and bargaining between the players. Our work removes the classical assumption that bargainers possess perfect knowledge of the underlying game. We first demonstrate that in the absence of property rights, the social welfare breaks down. We then design a policy for the players which allows them to learn a bargaining strategy which maximizes the total welfare, recovering the Coase theorem under uncertainty.

Incentivized Learning in Principal-Agent Bandit Games

This work considers a repeated principal-agent bandit game, where the principal can only interact with her environment through the agent. The principal and the agent have misaligned objectives and the choice of action is only left to the agent. However, the principal can influence the agent's decisions by offering incentives which add up to his rewards. The principal aims to iteratively learn an incentive policy to maximize her own total utility. This framework extends usual bandit problems and is motivated by several practical applications, such as healthcare or ecological taxation, where traditionally used mechanism design theories often overlook the learning aspect of the problem. We present nearly optimal (with respect to a horizon $T$) learning algorithms for the principal's regret in both multi-armed and linear contextual settings. Finally, we support our theoretical guarantees through numerical experiments.