Control games: the HON game model in Krivine's realisability

We show how the notion of games introduced recently by J.-L. Krivine
in its classical realisability is strongly related with the HON game
model.
A precise analysis of this correspondence allows us to simplify the
HON model of the lambda-mu calculus by the introduction of additional
pointers: control pointers (related with J. Laird's contingency
pointers). This model is equivalent to the appropriate version of the
non well-bracketed HON model, and thus fully complete for the
lambda-mu calculus. We give a direct proof of this full completeness
result.