Time-aware uniformization of winning strategies
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Two-player win/lose games of infinite duration are involved in several disciplines including computer science and logic. If such a game has deterministic winning strategies, one may ask how simple such strategies can get. The answer may help with actual implementation, or to win despite imperfect information, or to conceal sensitive information especially if the game is repeated. Given a game, this article considers equivalence relations over histories of played actions. A classical restriction used here is that equivalent histories have equal length, hence time awareness. A sufficient condition is given such that if a player has winning strategies, she has one that prescribes the same action at equivalent histories, hence uniformization. The proof is fairly constructive and preserves finiteness of strategy memory, and counterexamples show tightness of the result. Three corollaries follow for games with states and colors. They hold regardless of the winning condition.
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