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The main concern of this paper is to give simple determination of games and investigate the optimality ( ε -optimal) strategies (i.e., type of strategy) for each player in a new game, called Special Büchi game. We first review on extension version of reachability games, i.e., generalized reachability games. We next observe games with more complex objectives, games with Büchi objectives. We then introduce and study a new type of Büchi game called Special Büchi game. We define a new strategy, namely a finite memory strategy and provide various interesting results.

Finitely Memory Strategies in Special Büchi Games with Inductive Measurable Payoffs