Sequential games and optimal strategies

Abstract

This article gives an overview of recent work on the theory of selection functions. We explain the intuition behind these higher type objects, and define a general notion of sequential game whose optimal strategies can be computed via a certain product of selection functions. Several instances of this game are considered in a variety of areas such as fixed point theory, topology, game theory, higher type computability and proof theory. These examples are intended to illustrate how the fundamental construction of optimal strategies based on products of selection functions permeates several research areas.