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

Fighting terrorism: How to position rapid response teams?

In light of recent terrorist attacks, we introduce and study a Stackelberg game between a government and a terrorist. In this game, the government positions a number of heavily-armed rapid response teams on a line segment (e.g., a long boulevard or shopping avenue) and then the terrorist attacks a location with the highest potential impact of an attack. This potential impact, which we call damage, is the product of the time it takes the closest rapid response team to react and the damage caused per time unit, which is modeled via a damage rate function. We prove that there exists a subgame perfect Nash equilibrium that balances the possible damage on all intervals of the line segment that result from positioning the rapid response teams. We discuss the implications for various types of damage rate functions including one mimicking a busy boulevard with various hotspot locations

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