The risk-averse newsvendor game with competition on demand

Abstract

This paper studies the effect of risk-aversion in the competitive newsvendor game. Multiple newsvendors with risk-averse preferences face a random demand and the demand is allocated proportionally to their inventory levels. Each newsvendor aims to maximize his expected utility instead of his expected profit. Assuming a general form of risk-averse utility function, we prove that there exists a pure Nash equilibrium in this game, and it is also unique under certain conditions. We find that the order quantity of each newsvendor is decreasing in the degree of risk-aversion and increasing in the initial wealth. Newsvendors with moderate preferences of risk-aversion make more profits compared with the risk-neutral situation. We also discuss the joint effect of risk-aversion and competition. If the effect of risk-aversion is strong enough to dominate the effect of competition, the total inventory level under competition will be lower than that under centralized decision-making.