Behavioural equivalence of game descriptions

Game description language is a logical language designed for General Game Playing. The language is highly expressive so that, in theory, all finite-state games with perfect information and deterministic actions can be described. However, a game can be described in different ways and the way of description can dramatically affect behaviour of general game players. This paper investigates the relationships of game models and game descriptions. We first introduce the concept of submodel bisimulation to filter out unreachable states while maintain the nature of a game. We then define equivalence of game descriptions in the sense that two game descriptions are equivalent if the described games behaviourally the same. The concept of game equivalency, which breaks through logical equivalency, sets a boundary for reformulation of game descriptions. Finally we use a well-known strategy game, Hex Game, to demonstrate how to verify equivalence of game descriptions.