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CIO Springer TAP Compal BES FCT
SB3 Dynamic Games II
Session organizer: Georges Zaccour, GERAD, HEC Montréal, Canada

Chair: Georges Zaccour, GERAD, HEC Montréal, Canada
Room 3.1.11


Vertical and Horizontal Collaboration in Inventory and Transportation

Benedikt De Vos (, Birger Raa (
Road transportation companies continuously try to optimize their distribution activities. Collaboration in logistics offers promising opportunities to increase cost-efficiency of their activities while maintaining customer satisfaction. In this paper, two forms of collaboration in a decentralised supply chain are studied, namely vertical and horizontal collaboration through volumes and geographical area. First, vertical collaboration is introduced through Vendor Managed Inventory in order to coordinate inventory and distribution better and create higher cost-efficiency. Secondly, shippers are encouraged to collaborate horizontally by sharing their orders and replenishing retailers through jointly designed routes to create more efficient distribution. The transportation cooperation is established through a Logistics Service Provider. Several barriers to establishing successful collaboration are taken into account, such as the shippers' reluctance to collaborate and share sensitive information and the difficulty to guarantee sustainability of the collaboration over the long term. Once the cost savings are calculated, cooperative game theory is used to fairly allocate them to the coalition partners and guarantee sustainability of the collaboration. Given the complexity of the problem, focus is currently on small datasets.

Keywords: Supply chain management, Cooperative game theory, Inventory-Routing


Location game and applications in transportation networks

Vladimir Mazalov (, Yulia Tokareva (, Anna Shchiptsova (
We consider a market where the customers are distributed in the vertexes of a transportation graph. The edges of the graph are transportation links. The vertexes are the hubs. The customers are the passengers, who use this kind of transportation. The demand is determined by the flow of passengers. There are n companies (players), who make a service in this market. First, players form their transportation networks, and then they announce the prices for the service. The objective of a player is to maximize the payoff. We derive the equilibrium in this non-cooperative game. The results of numerical simulations are provided.

Keywords: location model, price competition, equilibrium


Feedback Nash Equilibria in Linear-Quadratic Difference Games with Constraints

Puduru Viswanadha Reddy (, Georges Zaccour (
In this paper, we consider a class of non-cooperative N-player finite-horizon linear-quadratic dynamic games with linear constraints. Assuming a constrained affine feedback information structure, we derive necessary conditions for the existence of feedback-Nash equilibria. We show that these conditions lead to a weakly coupled system of parametric value functions and parametric linear-complementarity problems. We show that these conditions can be reformulated as a single large-scale linear-complementarity problem. We provide a geometric interpretation of the results and give sufficient conditions for uniqueness of Nash equilibrium. We illustrate our results with a simple numerical example.

Keywords: Dynamic Games, Constrained Dynamic Programming, Feedback-Nash Equilibrium