  Game theory has been increasingly applied in settings where the game is not
known outright, but has to be estimated by sampling. For example, meta-games
that arise in multi-agent evaluation can only be accessed by running a
succession of expensive experiments that may involve simultaneous deployment of
several agents. In this paper, we focus on $\alpha$-rank, a popular
game-theoretic solution concept designed to perform well in such scenarios. We
aim to estimate the $\alpha$-rank of the game using as few samples as possible.
Our algorithm maximizes information gain between an epistemic belief over the
$\alpha$-ranks and the observed payoff. This approach has two main benefits.
First, it allows us to focus our sampling on the entries that matter the most
for identifying the $\alpha$-rank. Second, the Bayesian formulation provides a
facility to build in modeling assumptions by using a prior over game payoffs.
We show the benefits of using information gain as compared to the confidence
interval criterion of ResponseGraphUCB (Rowland et al. 2019), and provide
theoretical results justifying our method.
