Abstract
This paper is concerned with the complexity of computing winning strategies for poset games. While it is reasonably clear that such strategies can be computed in PSPACE, we give a simple proof of this fact by a reduction to the game of geography. We also show how to formalize the reasoning about poset games in Skelley’s theory $\mathbf{W}_{1}^{1}$ for PSPACE reasoning. We conclude that $\mathbf{W}_{1}^{1}$ can use the “strategy stealing argument” to prove that in poset games with a supremum the first player always has a winning strategy.
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