A General Framework for Cooperation under Uncertainty

In this paper, we introduce a general framework for situations with decision making under uncertainty and cooperation possibilities. This framework is based upon a two stage stochastic programming approach. We show that under relatively mild assumptions the cooperative games associated with these situations are totally balanced and, hence, have non-empty cores. Finally, we consider several example situations, which can be studied using this general framework.Two-stage stochastic programming;cooperative game theory;core

Supply chain collaboration

In the past, research in operations management focused on single-firm analysis. Its goal was to provide managers in practice with suitable tools to improve the performance of their firm by calculating optimal inventory quantities, among others. Nowadays, business decisions are dominated by the globalization of markets and increased competition among firms. Further, more and more products reach the customer through supply chains that are composed of independent firms. Following these trends, research in operations management has shifted its focus from single-firm analysis to multi-firm analysis, in particular to improving the efficiency and performance of supply chains under decentralized control. The main characteristics of such chains are that the firms in the chain are independent actors who try to optimize their individual objectives, and that the decisions taken by a firm do also affect the performance of the other parties in the supply chain. These interactions among firms’ decisions ask for alignment and coordination of actions. Therefore, game theory, the study of situations of cooperation or conflict among heterogenous actors, is very well suited to deal with these interactions. This has been recognized by researchers in the field, since there are an ever increasing number of papers that applies tools, methods and models from game theory to supply chain problems

Cooperation between Multiple Newsvendors with Warehouses

This study considers a supply chain that consists of n retailers, each of them facing a newsvendor problem, m warehouses and a supplier.The retailers are supplied with a single product via some warehouses.In these warehouses, the ordered amounts of goods of these retailers become available after some lead time.At the time that the goods arrive at the warehouses, demand realizations are known by the retailers.The retailers can increase their expected joint profits by coordinating their orders and making allocations after demand realization.For this setting, we consider an associated cooperative game between the retailers.We show that this associated cooperative game has a nonempty core. Finally, we study a variant of this game, where the retailers are allowed to leave unsold goods at the warehouses.supply chain management;newsvendor;warehouse;game theory;balancedness

A Note on Shapleys Convex Measure Games

L. S. Shapley, in his paper Cores of Convex Games, introduces Convex Measure Games, those that are induced by a convex function on R, acting over a measure on the coalitions. But in a note he states that if this function is a function of several variables, then convexity for the function does not imply convexity of the game or even superadditivity. We prove that if the function is directionally convex, the game is convex, and conversely, any convex game can be induced by a directionally convex function acting over measures on the coalitions, with as many measures as players.supermodularity, multilinear extension, convex cooperative games, directional convexity

On the Convexity of News Vendor Games

This study considers a simple newsvendor situation that consists of n retailers, all selling the same item with common purchasing costs and common selling prices.Groups of retailers might increase their expected joint profit by inventory centralization, which means that they make a joint order to satisfy total future demand.The resulting newsvendor games are shown to have non-empty cores in the literature.This study investigates convexity of newsvendor games.We focus our analysis on the class of newsvendor games with independent symmetric unimodal demand distributions after providing several examples outside this class that are not convex.Several interesting subclasses, containing convex games only, are identified.Additionally, we illustrate that these results can not be extended to all games in this class.game theory;inventory centralization;newsvendor;convexity

Joint ordering in multiple news-vendor problems : a game-theoretical approach

We study a situation with n retailers, each of them facing a news-vendor problem, i.e., selling to customers over a finite period of time (product with a short life cycle, such as fashion). Groups of retailers might improve their expected joint profit by cooperating. We analyze these situations by defining a cooperative game, called a general news-vendor game, for such a situation with n retailers. We concentrate on whether it makes sense to cooperate by studying properties of general news-vendor games. Besides some results on convexity we prove that general newsvendor games have non-empty cores, which answers an open question of Hartman et al. (2000)

A General Framework for Cooperation under Uncertainty

In this paper, we introduce a general framework for situations with decision making under uncertainty and cooperation possibilities. This framework is based upon a two stage stochastic programming approach. We show that under relatively mild assumptions the cooperative games associated with these situations are totally balanced and, hence, have non-empty cores. Finally, we consider several example situations, which can be studied using this general framework.

Inventory Games

AMS classifications: 90D12, 90B05.inventory management;information;cooperative games;proportional division