  We use a reformulation of compositional game theory to reunite game theory
with game semantics, by viewing an open game as the System and its choice of
contexts as the Environment. Specifically, the system is jointly controlled by
$n \geq 0$ noncooperative players, each independently optimising a real-valued
payoff. The goal of the system is to play a Nash equilibrium, and the goal of
the environment is to prevent it. The key to this is the realisation that
lenses (from functional programming) form a dialectica category, which have an
existing game-semantic interpretation.
  In the second half of this paper, we apply these ideas to build a compact
closed category of `computable open games' by replacing the underlying
dialectica category with a wave-style geometry of interaction category,
specifically the Int-construction applied to the cartesian monoidal category of
directed-complete partial orders.
