Strategy Composition in Compositional Games
When studying games played on finite arenas, the arena is given explicitly, hiding the underlying structure of the arena. We study games where the global arena is a product of several smaller, constituent arenas. We investigate how these “global games” can be solved by playing “component games” on the constituent arenas. To this end, we introduce two kinds of products of arenas. Moreover, we define a suitable notion of strategy composition and show how, for the first notion of product, winning strategies in reachability games can be composed from winning strategies in games on the constituent arenas. For the second kind of product, the complexity of solving the global game shows that a general composition theorem is equivalent to proving Pspace = Exptime.
KeywordsTuring Machine Winning Strategy Reachability Condition Positional Strategy Polynomial Size
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