Decentralized Inventory Transshipments with Quantal Response Equilibrium

Abstract

Despite the benefits of inventory transshipment, numerous behavioral experiments have revealed that retailers often deviate from the Nash-equilibrium ordering quantities, which in turn impacts the potential advantages. Motivated by this issue, we developed a behavioral model to analyze the deviation of ordering quantities among two independent retailers who engage in inventory transshipment from the perspective of analytical modeling. In our model, we incorporated bounded rationality with the quantal response equilibrium. Firstly, we established the existence of such a quantal response equilibrium and provided the conditions for its uniqueness. Secondly, we compared the quantal response equilibrium with the Nash equilibrium within a certain range of transshipment prices and observed that the limiting quantal response equilibrium is equivalent to the Nash equilibrium. Lastly, we design an iterative algorithm that incorporates the learning effects of the retailers to determine the quantal response equilibrium for the ordering quantity. The results indicate that the optimal ordering quantity and the nearby ordering quantities should be chosen with higher probabilities. Additionally, the retailer should gradually enhance their cognitive or computational abilities through repeated transshipment games to improve their decision-making process. Furthermore, to ensure a balanced inventory-sharing system, the evaluation of inventory strategies should consistently prioritize avoiding surplus instead of shortage.

Keywords

• Nash equilibrium
• transshipment
• quantal response equilibrium
• bounded rationality