This paper aims to apply the real options game theoretic to study the impact of sudden events on the optimal investment timing and capacity choice in a duopoly market. We model the market demand and investment cost as the geometric Brownian motions with jumps driven by the Poisson processes. A new computing method independent on specific distribution functions is proposed for the real option models with jump processes of random frequency and amplitude. Based on this method, we find that both firms delay investment with a larger capacity as uncertainties of demand and investment cost increase. We also demonstrate that two firms both invest later and the optimal capacity relationship between them is ambiguous in the presence of two sources of uncertainty. Numerical simulation reveals that upward (downward) jump in demand and downward (upward) jump in investment cost cause the firms to invest earlier (later) with a larger (smaller) capacity. Finally, in a duopoly with symmetric firms, the first investor invests earlier than in an asymmetric duopoly due to the threat of preemption.
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