Long-term causal effects of interventions in multiagent economic mechanisms

The effect of an intervention in an economic mechanism, for example an increase in the reserve price of an auction, is causal if the observed effect is better than the counterfactual, i.e., the effect that would be observed under no intervention. As mechanisms are populated by dynamical systems of interacting agents, their response to an intervention fluctuates until the system reaches a new equilibrium. Effects measured in the new equilibrium, the long-term causal effects, are more representative of the value of interventions. However, the statistical estimation of long-term causal effects is difficult because it has to rely, for practical reasons, on data observed before the new equilibrium is reached. Furthermore, agent actions do not only depend on the mechanism that the agents are situated in but also on the behavior of others, which complicates the causal evaluation. In this paper, we formalize this problem of estimating long-term causal effects under the potential outcomes framework of causal inference \cite{neyman1923, rubin74}. We develop an estimation method that relies on a data augmentation strategy, where agents are assumed to adopt, at each timepoint, a behavior that is latent. This allows us to leverage existing work in behavioral game theory and time-series analysis of compositional data. Our method identifies the long-term causal effects under a set of assumptions that we formulate explicitly. We illustrate our method on a dataset from a real-world behavioral experiment, and discuss open problems to stimulate future research.