Jeux abstraits et composition catégorique
Michel Hirschowitz · HAL (Le Centre pour la Communication Scientifique Directe) · 2004
In this thesis, we propose a new notion of game, which we call team game, obtained by extracting the essence of the notion introduced by Hyland and Ong. In a team game, we have natural geometric notions of position, move, play, and strategy. Among positions, we distinguish winning and losing ones, and among strategies, we distinguish winning and deterministic ones. Composition, which allows players to combine their strategies in order to split the common goal into complementary parts, is the main feature of a team game. This composition has neutral elements and satisfies the natural associativity condition. Moreover, winning and deterministic strategies are stable by composition. As a main example, we give a team game corresponding to the HO-games, where objects are plays in some arena.