Human and Machine Intelligence in n-Person Games with Partial Knowledge

In this note, I introduce a new framework called n-person games with partial knowledge, in which players have only limited knowledge about the aspects of the game -- including actions, outcomes, and other players. For example, playing an actual game of chess is a game of partial knowledge. To analyze these games, I introduce a set of new concepts and mechanisms for measuring the intelligence of players, with a focus on the interplay between human- and machine-based decision-making. Specifically, I introduce two main concepts: firstly, the Game Intelligence (GI) mechanism, which quantifies a player's demonstrated intelligence in a game by considering not only the game's outcome but also the "mistakes" made during the game according to the reference machine's intelligence. Secondly, I define gaming-proofness, a practical and computational concept of strategy-proofness. The GI mechanism provides a practicable way to assess players and can potentially be applied to a wide range of games, from chess and backgammon to AI systems. To illustrate the GI mechanism, I apply it to an extensive dataset comprising over a million moves made by top chess Grandmasters.