Butwellafterconvergence this flips and policy change is relatively high in these states. In Section 3.3 we already touched on this subject with the experiments onCATCH using value iteration. In this section we revisit the question and try to provide a more definite answer to it. Itiswellknownthatlimk Tkπq =qπ foranyq Q. Equipped with the concepts above, we can now present our example. Clearly,inthe first step, when we change fromπ to π1 = g(T1π qπ), the policy changes ins from redto green.

We characterise the phenomenon empirically, verifying that it is not limited to specific algorithm or environment properties.

To learn good joint policies for multi-agent collaboration with incomplete information remains a fundamental challenge.

Planned experiments are the gold standard in reliably comparing the causal effect of switching from a baseline policy to a new policy. One critical shortcoming of classical experimental methods, however, is that they typically do not take into account the dynamic nature of response to policy changes. For instance, in an experiment where we seek to understand the effects of a new ad pricing policy on auction revenue, agents may adapt their bidding in response to the experimental pricing changes. Thus, causal effects of the new pricing policy after such adaptation period, the long-term causal effects, are not captured by the classical methodology even though they clearly are more indicative of the value of the new policy. Here, we formalize a framework to define and estimate long-term causal effects of policy changes in multiagent economies. Central to our approach is behavioral game theory, which we leverage to formulate the ignorability assumptions that are necessary for causal inference. Under such assumptions we estimate long-term causal effects through a latent space approach, where a behavioral model of how agents act conditional on their latent behaviors is combined with a temporal model of how behaviors evolve over time.

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We characterise the phenomenon empirically, verifying that it is not limited to specific algorithm or environment properties.

To learn good joint policies for multi-agent collaboration with imperfect information remains a fundamental challenge.

Therefore, our paper could have stronger implications than we expect. We disagree with R2 that the tabular form of JPS indeed has theoretical guarantees, as appreciated by other reviewers. Full game AI is a future work. This change leads to very different (and novel) theoretical insights. It leads to policy-change decomposition in Thm. 1, We will add comparisons in the next version.