R. Ramanujam and Sunil Simon
Logic, Navya-Nyaya & Applications . Studies in Logic, volume 15, pages 261-286, College Publications, London, 2008.
We present a quick summary of formal reasoning about games in logics, pointing out that strategies (which are the core of game playing) are mostly treated as being atomic (unstructured). While this is adequate for reasoning "from above", where one is interested in the logical structure of the game itself, or that of removing dominated strategies, or existence of equilibria, it offers little help for how to play. When it comes to reasoning within the game, a player's choice of strategy depends not only on her knowledge of the game position but also her expectation of the strategies employed by other players of which she can only have partial knowledge. Moreover, strategies are completely known to players only in small games where a strategy amounts to picking a small number of moves; in games with rich structure, intricate reasoning about strategies can be called for. This article is intended as an (expository) account of only the main issues, with detailed proofs to be found in the referenced literature.