Game Theoretic Rating in n-player general-sum games with Equilibria

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, 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. 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 multi-agent training and real-world interactions between many agents. Based on match-up data from 2018/2019 Premier League, we identify real-life non-transitivities and demonstrate how a club's ratings are affected by their success against members in the cycle, and the extent to which teams capitalize on home advantage.