On values of games

Abstract

In this paper, we present some recent results of infinite games played on a finite graph. We mainly work with generalized reachability games and Büchi games. These games are two-player concurrent games in which each player chooses simultaneously their moves at each step.We concern here with a description of winning strategies and payoff functions over infinite plays. Each play and the outcome of a game are completely determined by strategies of the players. We classify strategies regarding their use of history. Our goal is to give simple expressions of values for each game. Moreover, we are interested in the question of what type of optimal (ɛ-optimal) strategy exists for both players depending on the type of games.