  Rating strategies in a game is an important area of research in game theory
and artificial intelligence, and can be applied to any real-world competitive
or cooperative setting. Traditionally, only transitive dependencies between
strategies have been used to rate strategies (e.g. Elo), however recent work
has expanded ratings to utilize game theoretic solutions to better rate
strategies in non-transitive games. This work generalizes these ideas and
proposes novel algorithms suitable for N-player, general-sum rating of
strategies in normal-form games according to the payoff rating system. This
enables well-established solution concepts, such as equilibria, to be leveraged
to efficiently rate strategies in games with complex strategic interactions,
which arise in multiagent training and real-world interactions between many
agents. We empirically validate our methods on real world normal-form data
(Premier League) and multiagent reinforcement learning agent evaluation.
