Peter Borm

On the position value for communication situations

A new solution concept for communication situations is considered: the position value. This concept is based on an evaluation of the importance of the various communication links between the players. An axiomatic characterization of the position value is provided for the class of communication situations where the communication graphs contain no cycles. Furthermore, relations with the Myerson value are discussed,and, for special classes of communication situations, elegant calculation methods for their position values are described.

Operations Research Games: A Survey

This paper surveys the research area of cooperative games associated with several types of operations research problems in which various decision makers (players) are involved. Cooperating players not only face a joint optimisation problem in trying, e.g., to minimise total joint costs, but also face an additional allocation problem in how to distribute these joint costs back to the individual players. This interplay between optimisation and allocation is the main subject of the area of operations research games. It is surveyed on the basis of a distinction between the nature of the underlying optimisation problem: connection, routing, scheduling, production and inventory.

Economic Lot-Sizing Games

In this paper we introduce a new class of OR games: economic lot-sizing (ELS) games. There are a number of retailers that have a known demand for a fixed number of periods. To satisfy demand the retailers order products at the same manufacturer. By placing joint orders instead of individual orders, costs can be reduced and a cooperative game arises. In this paper we show that ELS games are balanced. Furthermore, we show that two special classes of ELS games are concave.

CONGESTION GAMES AND POTENTIALS RECONSIDERED

In congestion games, players use facilities from a common pool. The benefit that a player derives from using a facility depends, possibly among other things, on the number of users of this facility. The paper gives an easy alternative proof of the isomorphism between exact potential games and the set of congestion games introduced by Rosenthal (1973). It clarifies the relations between existing models on congestion games, and studies a class of congestion games where the sets of Nash equilibria, strong Nash equilibria and potential-maximizing strategies coincide. Particular emphasis is on the computation of potential-maximizing strategies.

On games corresponding to sequencing situations with ready times

This paper considers the special class of cooperative sequencing games that arise from one-machine sequencing situations in which all jobs have equal processing times and the ready time of each job is a multiple of the processing time.By establishing relations between optimal orders of subcoalitions, it is shown that each sequencing game within this class is convex.

Cooperation and competition in inventory games

Abstract. Inventory cost games are introduced in Meca et al. (1999). These games arise when considering the possibility of joint ordering in n-person EOQ inventory situations. Moreover, the SOC-rule is introduced and analysed as a cost allocation rule for this type of situations. In the current paper it is seen that n-person EPQ situations with shortages lead to exactly the same class of cost games. Furthermore, an alternative characterization of the SOC-rule is offered, primarily based on a transfer property which constitutes a special form of additivity. Necessary input variables for the SOC-rule are the (optimal) individual average number of orders per time unit in case there is no cooperation. Assuming that these average numbers are observable but not verifiable, we allow the players to select them strategically, while knowing that the SOC-rule will be (consecutively) applied as the cost allocation principle. Necessary and sufficient conditions are provided for the existence (and uniqueness) of a so-called constructive equilibrium in which all players make joint orders.

Simple Priorities and Core Stability in Hedonic Games

In this paper we study hedonic games where each player views every other player either as a friend or as an enemy. Two simple priority criteria for comparison of coalitions are suggested, and the corresponding preference restrictions based on appreciation of friends and aversion to enemies are considered. We characterize internally stable coalitions on the proposed domains and show how these characterizations can be used for generating a strict core element in the first case and a core element in the second case. Moreover, we prove that an element of the strict core under friends appreciation can be found in polynomial time, while finding an element of the core under enemies aversion is NP-hard.

The Myerson value for union stable structures

We study cooperation structures with the following property: Given any two feasible coalitions with non-empty intersection, its union is a feasible coalition again. These combinatorial structures have a direct relationship with graph communication situations and conference structures à la Myerson. Characterizations of the Myerson value in this context are provided using the concept of basis for union stable systems. Moreover, TU-games restricted by union stable systems generalizes graph-restricted games and games with permission structures.

Supplier-initiated outsourcing: A methodology to exploit synergy in transportation

Over the last decades, transportation has been evolving from a necessary, though low priority function to an important part of business that can enable companies to attain a competitive edge over their competitors. To cut down transportation costs, shippers often outsource their transportation activities to a logistics service provider of their choice. This paper proposes a new procedure that puts the initiative with the service provider instead: supplier-initiated outsourcing. This procedure is based on both operations research and game theoretical insights. To stress the contrast between the traditional push approach of outsourcing, and the here proposed pull approach where the service provider is the initiator of the shift of logistics activities from the shipper to the logistics service provider, we will refer to this phenomenon as insinking. Insinking has the advantage that the logistics service provider can proactively select a group of shippers with a strong synergy potential. Moreover, these synergies can be allocated to the participating shippers in a fair and sustainable way by means of a so-called Shapley Monotonic Path of customized tariffs. Insinking is illustrated by means of a practical example based on data from the Dutch grocery transportation sector.

On the convexity of communication games

A communication situation consists of a game and a communication graph. By introducing two different types of corresponding communication games, point games and arc games, the Myerson value and the position value of a communication situation were introduced.This paper investigates relations between convexity of the underlying game and the two communication games. In particular, assuming the underlying game to be convex, necessary and sufficient conditions on the communication graph are provided such that the communication games are convex. Moreover, under the same conditions, it is shown that the Myerson value and the posi tion value are in the core of the point game. Some remarks are made on superadditivity and balancedness.