A two-player newsvendor game with competition on demand under ambiguity

We deal with a single period two-player newsvendor game where both newsvendors are assumed to be rational and risk-neutral, and to operate under ambiguity. Each newsvendor needs to choose his/her order quantity of the same perishable product, whose global market demand is modeled by a discrete random variable, endowed with a reference probability measure. Furthermore, the global market demand is distributed to newsvendors according to a proportional allocation rule. We model the uncertainty faced by each newsvendor with an individual epsilon-contamination of the reference probability measure, computed with respect to a suitable class of probability measures. The resulting epsilon-contamination model preserves the expected demand under the reference probability and is used to compute the individual lower expected profit as a Choquet expectation. Therefore, the optimization problem of each player reduces to settle the order quantity that maximizes his/her lower expected profit, given the opponent choice, which is a maximin problem. In the resulting game, we prove that a Nash equilibrium always exists, though it may not be unique. Finally, we provide a characterization of Nash equilibria in terms of best response functions.