Borel Determinacy of Concurrent Games

Abstract

Just as traditional games can be represented by trees, so concurrent games can be represented by event structures. We show the determinacy of such concurrent games with Borel sets of configurations as winning conditions, provided they are race-free and bounded-concurrent. Both properties are shown necessary. The determinacy proof proceeds via a reduction to the determinacy of tree games, and the determinacy of these in turn reduces to the determinacy of Gale-Stewart games.