  We present a method of backward induction for computing approximate subgame
perfect Nash equilibria of infinitely repeated games with discounted payoffs.
This uses the selection monad transformer, combined with the searchable set
monad viewed as a notion of 'topologically compact' nondeterminism, and a
simple model of computable real numbers. This is the first application of
Escard\'o and Oliva's theory of higher-order sequential games to games of
imperfect information, in which (as well as its mathematical elegance) lazy
evaluation does nontrivial work for us compared with a traditional
game-theoretic analysis. Since a full theoretical understanding of this method
is lacking (and appears to be very hard), we consider this an 'experimental'
paper heavily inspired by theoretical ideas. We use the famous Iterated
Prisoner's Dilemma as a worked example.
