Robust Multi-agent Counterfactual Prediction

Abstract

We consider the problem of using logged data to make predictions about what would happen if we changed the 'rules of the game' in a multi-agent system. This task is difficult because in many cases we observe actions individuals take but not their private information or their full reward functions. In addition, agents are strategic, so when the rules change, they will also change their actions. Existing methods (e.g. structural estimation, inverse reinforcement learning) make counterfactual predictions by constructing a model of the game, adding the assumption that agents' behavior comes from optimizing given some goals, and then inverting observed actions to learn agent's underlying utility function (a.k.a. type). Once the agent types are known, making counterfactual predictions amounts to solving for the equilibrium of the counterfactual environment. This approach imposes heavy assumptions such as rationality of the agents being observed, correctness of the analyst's model of the environment/parametric form of the agents' utility functions, and various other conditions to make point identification possible. We propose a method for analyzing the sensitivity of counterfactual conclusions to violations of these assumptions. We refer to this method as robust multi-agent counterfactual prediction (RMAC). We apply our technique to investigating the robustness of counterfactual claims for classic environments in market design: auctions, school choice, and social choice. Importantly, we show RMAC can be used in regimes where point identification is impossible (e.g. those which have multiple equilibria or non-injective maps from type distributions to outcomes). * Equal contribution, author order has been randomized.

Robust Market Equilibria with Uncertain Preferences

“…We consider the case of low rank markets (Kroer et al, 2019;Peysakhovich and Kroer, 2019). In these markets, the valuations individuals place on items are not independent, and can be predicted from one another; this is common in most real-world allocation problems (e.g.…”

“…A similar uncertainty-parametrization of utilities was considered by Aghassi and Bertsimas (2006) in the context of game-theoretic equilibrium where they provide a robust analogue of Bayesian equilibrium. Robust game-theoretic equilibria have also been considered in the context of counterfactual prediction (Peysakhovich, Kroer, and Lerer, 2019). Finally, there is literature on robust mechanism design (Bergemann and Morris, 2005;Lopomo, Rigotti, and Shannon, 2018;Albert et al, 2017), where the goal is to design mechanisms that are robust either to uncertainty about the distribution over agent payoffs, or the belief that an agent holds about the types of other agents.…”

Counterfactual Thinking in Cooperation Dynamics

“…Foerster et al [18] addressed cases where counterfactual thinking consists in imagining changes in the rules of the game, an interesting problem not addressed in this chapter. Peysakhovich et al [19] rely on the availability and use of a centralized critic that estimates counterfactual advantages for the multi-agent system by reinforcement learning policies. While interesting from a engineering perspective, it differs significantly from our work, in that we have no central critic, no utility function to be maximized, nor the aim of conjuring a policy that optimizes given utility function.…”