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We investigate determinacy of delay games with Borel winning conditions,infinite-duration two-player games in which one player may delay her moves toobtain a lookahead on her opponent's moves.  First, we prove determinacy of such games with respect to a fixed evolutionof the lookahead. However, strategies in such games may depend on informationabout the evolution. Thus, we introduce different notions of universalstrategies for both players, which are evolution-independent, and determine theexact amount of information a universal strategy needs about the history of aplay and the evolution of the lookahead to be winning. In particular, we showthat delay games with Borel winning conditions are determined with respect touniversal strategies. Finally, we consider decidability problems, e.g., "Does aplayer have a universal winning strategy for delay games with a given winningcondition?", for omega-regular and omega-context-free winning conditions.

What are Strategies in Delay Games? Borel Determinacy for Games with Lookahead