A Theory for Game Theories

Abstract. We explain a double-category (of positions and plays) attached to the theory of HOgames (those with the so-called switching condition [7]) from which the category of arenas and strategies can be recovered in a natural way. Then we explain how HO-games appear as an instance of a more general construction: we show how a double-category of positions and plays and thus a category of positions and strategies can be constructed from still less data: roughly a category equipped with some king of signs and two selections of odd morphisms (moves). This yields a generalized notion of game equipped with the familiar notions of position, move, play, and strategy. Among positions there are winning and losing ones, and among strategies, there are deterministic and winning ones. The central feature of our categorical games is the composition of strategies which models how two players combine their strategies dedicated to two complementary goals, yielding a common strategy against the combin...

• Type: Conference
• Year: 2007
• Where: FSTTCS
• Authors: Michel Hirschowitz, André Hirschowitz, Tom Hirschowitz
• Keywords: FSTTCS 2007, Positions, So-called Switching Condition, Strategies