Human and Machine: Practicable Mechanisms for Measuring Performance in Partial Information Games

In this note, I introduce a new framework called $n$-person general-sum games with partial information, in which boundedly rational players have only limited information about the game -- including actions, outcomes, and other players. For example, playing an actual game of chess is a game of partial information. To analyze these games, I introduce a set of new concepts and metrics for measuring the performance of players, with a focus on the interplay between human- and machine-based decision-making. Specifically, I introduce (i) gaming-proofness, which is a property of a mechanism that players cannot game from a practical perspective, and (ii) the Net Game Points (NGP) mechanism, which measures the success of a player's performance in a game, taking into account both the outcome of the game and the ``mistakes'' made during the game. The NGP mechanism provides a practicable way to assess game outcomes and can potentially be applied to a wide range of games, from poker and football to AI systems, organizations, and companies. To illustrate the concept, I apply the NGP mechanism to select chess games played between some of the world's top players, including the world champion.