Abstract
We have a simple theory of strategy for generalized Shannon switching games (on edges). This theory naturally gives us an algorithm of polynomial order. On the other hand Reisch states the PSPACE completeness of judging who can win in all the positions of Hex. Our purpose in this paper is to discuss the difficulty not of a class but of each particular game. We shall see that any strategy theory of a certain type cannot be applied either to Hex of 4 2 vertices or to a certain 3-pair game, though it can be applied to all 2-pair games. Here, an n-pair game is a game played on the edge set of a graph where a designated player intends to connect at least one of the given n pairs of terminals.
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