In a social system, the self-interest of agents can be detrimental to the collective good, sometimes leading to social dilemmas. To resolve such a conflict, a central designer may intervene by either redesigning the system or incentivizing the agents to change their behaviors. To be effective, the designer must anticipate how the agents react to the intervention, which is dictated by their often unknown payoff functions. Therefore, learning about the agents is a prerequisite for intervention. In this paper, we provide a unified framework for learning and intervention in games. We cast the equilibria of games as individual layers and integrate them into an end-to-end optimization framework.

Correctness: I don't see any problems with the empirical methodology. There are a few claims that seem somewhat misleading, possibly due to lack of clarity in writing. For example, in subsection 3.2.1, after discussing requirements for the convergence of the projection method, the authors state "Therefore, a sufficiently small r can guarantee convergence for projection methods in general". It's unclear what context this should be read in, but this contradicts the monotone setting mentioned earlier. However, the former may not generate a solution to the VI whereas the latter obviously does so the claim is at least misleading.

In a social system, the self-interest of agents can be detrimental to the collective good, sometimes leading to social dilemmas. To resolve such a conflict, a central designer may intervene by either redesigning the system or incentivizing the agents to change their behaviors. To be effective, the designer must anticipate how the agents react to the intervention, which is dictated by their often unknown payoff functions. Therefore, learning about the agents is a prerequisite for intervention. In this paper, we provide a unified framework for learning and intervention in games. We cast the equilibria of games as individual layers and integrate them into an end-to-end optimization framework.