Infinite horizon extensive form games, coalgebraically

Nash equilibrium in every subgame of the game. In a series of papers, Douglas Bridges investigated constructive aspects of the theory of games where players move simultaneously (so-called normal form games), and their preference relations. This article is concerned with a constructive treatment of games where players move sequentially. A common way to model sequential games is using their extensive form: a game is represented as a tree, whose branching structure reflects the decisions available to the players, and whose leaves (corresponding to a complete 'play' of the game) are decorated by payoffs for each player. When the number of rounds in the game is infinite (e.g. because a finite game is repeated an infinite number of times, or because the game may continue forever), the game tree needs to be infinitely deep. One way to handle such infinite trees is to consider them as the metric completion of finite trees, after equipping them with a suitable metric. However, as a definitional principle, this only gives a method to construct functions into other complete metric spaces, and the explicit construction as a quotient of Cauchy sequences can be unwieldy to work with. Instead, we prefer to treat the infinite as the dual of the finite, in the spirit of category theory and especially the theory of coalgebras.