In this paper, I formalize intelligence measurement in games by introducing mechanisms that assign a real number -- interpreted as an intelligence score -- to each player in a game. This score quantifies the ex-post strategic ability of the players based on empirically observable information, such as the actions of the players, the game's outcome, strength of the players, and a reference oracle machine such as a chess-playing artificial intelligence system. Specifically, I introduce two main concepts: first, the Game Intelligence (GI) mechanism, which quantifies a player's 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. Second, I define gamingproofness, a practical and computational concept of strategyproofness. To illustrate the GI mechanism, I apply it to an extensive dataset comprising over a billion chess moves, including over a million moves made by top 20 grandmasters in history. Notably, Magnus Carlsen emerges with the highest GI score among all world championship games included in the dataset. In machine-vs-machine games, the well-known chess engine Stockfish comes out on top.

翻译：本文通过引入一种机制，将博弈中每位玩家的表现量化为实数（即智能得分），实现了对博弈智能的形式化度量。该得分基于经验可观测信息（如玩家行为、博弈结果、玩家实力及参考预言机（如国际象棋人工智能系统））量化玩家的事后战略能力。具体而言，本文提出两个核心概念：第一，博弈智能机制——通过考虑博弈结果以及根据参考机器智能判定的“失误”来量化玩家在博弈中的智能水平；第二，博弈抗操纵性——一种实用且可计算的策略抗操纵性概念。为阐明博弈智能机制，本文将其应用于包含超十亿步国际象棋棋步的庞大数据集（含历史前20位特级大师逾百万步棋步）。值得注意的是，在该数据集所有世界冠军赛中，马格努斯·卡尔森的博弈智能得分最高；在机器对弈中，知名国际象棋引擎Stockfish脱颖而出。