This paper provides theoretical bounds for empirical game theoretical
analysis of complex multi-agent interactions. We provide insights in the
empirical meta game showing that a Nash equilibrium of the meta-game is an
approximate Nash equilibrium of the true underlying game. We investigate and
show how many data samples are required to obtain a close enough approximation
of the underlying game. Additionally, we extend the meta-game analysis
methodology to asymmetric games. The state-of-the-art has only considered
empirical games in which agents have access to the same strategy sets and the
payoff structure is symmetric, implying that agents are interchangeable.
Finally, we carry out an empirical illustration of the generalised method in
several domains, illustrating the theory and evolutionary dynamics of several
versions of the AlphaGo algorithm (symmetric), the dynamics of the Colonel
Blotto game played by human players on Facebook (symmetric), and an example of
a meta-game in Leduc Poker (asymmetric), generated by the PSRO multi-agent
learning algorithm.Comment: will appear at AAMAS'1
