Robust Newsvendor Competition

We analyze competition among newsvendors when the only information competitors possess about the nature of future demand realizations is the support of demand distributions. In such a setting, traditional expectation-based optimization criteria may not be adequate. In our analysis, we focus on several alternative criteria used in the robust optimization literature, such as relative and absolute regret, as well as worst-case performance. Using these robust criteria, we establish the unique Nash equilibrium solution for a (symmetric) game with an arbitrary number of players. In addition, we obtain closed-form, intuitive expressions for the optimal order quantities which allow us to gain insight into the nature of robust competition. We show that the ex-ante and ex-post versions of the competitive newsvendor problem are equivalent under the worst-case or the absolute regret or the relative regret criterion. Numerical analysis indicates that, among different robust approaches, absolute regret minimization offers the most sensible alternative when demand distribution is unknown.