  In this paper, we propose a discretization scheme for the two-stage
stochastic linear complementarity problem (LCP) where the underlying random
data are continuously distributed. Under some moderate conditions, we derive
qualitative and quantitative convergence for the solutions obtained from
solving the discretized two-stage stochastic LCP (SLCP). We explain how the
discretized two-stage SLCP may be solved by the well-known progressive hedging
method (PHM). Moreover, we extend the discussion by considering a two-stage
distributionally robust LCP (DRLCP) with moment constraints and proposing a
discretization scheme for the DRLCP. As an application, we show how the SLCP
and DRLCP models can be used to study equilibrium arising from two-stage
duopoly game where each player plans to set up its optimal capacity at present
with anticipated competition for production in future.
