This paper introduces a model of IMLAL, the intuitionistic
multiplicative fragment of Light Affine Logic, based on games and
discreet strategies. We define a generalised notion of threads, so
that a play of a game (of depth k) may be regarded as a number of
interwoven threads (of depths ranging from 1 to k). To constrain the
way threads communicate with each other, we organise them into
networks at each depth (up to k), in accord with a protocol:
* A network comprises an O-thread (which can only be created by O) and
finitely many P-threads (which can only be created by P).
* A network whose O-thread arises from a shriek-game can have at most
one P-thread which must also arise from a shriek-game.
* No thread can belong to more than one network.
* Only O can switch between networks, and only P can switch between
threads within the same network.
Strategies that comply with the protocol are called discreet, and they
give rise to a fully complete model of IMLAL. Since IMLAL has a
polytime cut-elimination procedure, the model gives a basis for a
denotational-semantic characterisation of PTIME.
