Productivity of paracompactness in the class of GO-spaces

The main result of the paper says that if X is a paracompact GO-space, meaning a subspace of a linearly ordered space and M a paracompact space satisfying the first axiom of countability such that X can be embedded in M ω 1 then the product X × Y is paracompact for every paracompact space Y if and only if the first player of the G ( D C , X ) game, introduced by Telgarsky has a winning strategy. In particular we obtain that if X is paracompact GO-space of weight not greater than ω 1 then the product X × Y is paracompact for every paracompact space Y if and only if the first player of the G ( D C , X ) game has a winning strategy.