A Dual Egalitarian Solution

In this note we introduce an egalitarian solution, called the dual egalitarian solution, that is the natural counterpart of the egalitarian solution of Dutta and Ray (1989). We prove, among others, that for a convex game the egalitarian solution coincides with the dual egalitarian solution for its dual concave game.Concave Games

On the core of m-attribute games

We study a special class of cooperative games with transferable utility (TU), called (Formula presented.) -attribute games. Every player in an (Formula presented.) -attribute game is endowed with a vector of (Formula presented.) attributes that can be combined in an additive fashion; that is, if players form a coalition, the attribute vector of this coalition is obtained by adding the attributes of its members. Another fundamental feature of (Formula presented.) -attribute games is that their characteristic function is defined by a continuous attribute function (Formula presented.) —the value of a coalition depends only on evaluation of (Formula presented.) on the attribute vector possessed by the coalition, and not on the identity of coalition members. This class of games encompasses many well-known examples, such as queueing games and economic lot-sizing games. We believe that by studying attribute function (Formula presented.) and its properties, instead of specific examples of games, we are able to develop a common platform for studying different situations and obtain more general results with wider applicability. In this paper, we first show the relationship between nonemptiness of the core and identification of attribute prices that can be used to calculate core allocations. We then derive necessary and sufficient conditions under which every (Formula presented.) -attribute game embedded in attribute function (Formula presented.) has a nonempty core, and a set of necessary and sufficient conditions that (Formula presented.) should satisfy for the embedded game to be convex. We also develop several sufficient conditions for nonemptiness of the core of (Formula presented.) -attribute games, which are easier to check, and show how to find a core allocation when these conditions hold. Finally, we establish natural connections between TU games and (Formula presented.) -attribute games.</p

A competitive solution for cooperative truckload delivery

This paper introduces a solution for gain sharing in consortia of logistic providers where joint planning of truckload deliveries enables the reduction of empty kilometers. The highly competitive nature of freight transport markets necessitates solutions that distinguish among the logistics providers based on their characteristics, even in situations with two players only. We introduce desirable properties in these situations and propose a solution that satisfies such properties. By comparing the existing solutions against the introduced properties we demonstrate the advantages of our proposed solution

Distribution center consolidation games

We study the location-inventory model as introduced by Teo et al. (2001) to analyze the impact of consolidation of distribution centers on facility and inventory costs. We extend their result on profitability of consolidation. We associate a cooperative game with each location-inventory situation and prove that this game has a non-empty core for identical and independent demand processes. This illustrates that consolidation does not only lower joint costs (which was shown by Teo et al. (2001)), but it allows for a stable division of the minimal costs as well

A cooperative appproach to queue allocation of indivisible objects

We consider the allocation of a finite number of indivisible objects to the same number of agents according to an exogenously given queue. We assume that the agents collaborate in order to achieve an efficient outcome for society. We allow for side-payments and provide a method for obtaining stable outcomes

Collaborative replenishment in the presence of intermediaries

In complex supply chains, downstream buyers would often replenish individually from intermediaries instead of directly dealing with original manufacturers. Although collaborative replenishment from intermediaries might generate benefits, significant cost reductions could be achieved when direct replenishments from manufacturers are considered. This paper constructs a general model to study collaborative replenishment in multi-product chains with alternative sources of supply—i.e., manufacturers and intermediaries. A collaborative organization determines the optimal choices of replenishment sources on behalf of its members to minimize collective costs. We introduce a class of cooperative games associated with these situations and give sufficient conditions for their concavity. We investigate the choice of allocation rule and its effect on supply chain efficiency when buyers strategically participate in the collaborative organization. We prove that the Shapley value coordinates the supply chain, i.e., it makes complete participation the best strategy for buyers even under asymmetric information. This setting is compared with an alternative structure where buyers can only collaborate in source-specific replenishment organizations that purchase all requested products either from intermediaries or manufacturers. Although there are always participation strategies that result in minimum collective cost, it is impossible to find allocation rules for source-specific replenishment organizations that always motivate the buyers to choose such strategies