Game Theory's Basic Question: Who Is a Player?

The paper introduces and discusses some of the most important conceptual ideas in game theory by exploring their implicit answer to the question: Who is a player? It will be illustrated that some of the most celebrated results in game theory rely on different notions of a player, global players or more independent local decision-makers. The examples are the durable monopoly game, the Folk Theorem for supergames, forward induction solutions for outside option games and games with incomplete information. We also discuss the empirical relevance of the game theoretic concepts, mostly by briefly reviewing some related experimental results.