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

Discrete Approximation of Two-Stage Stochastic and Distributionally Robust Linear Complementarity Problems