Ruud Hendrickx

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.

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.

Paired comparisons analysis: an axiomatic approach to ranking methods

In this paper we present an axiomatic analysis of several ranking methods for general tournaments. We find that the ranking method obtained by applying maximum likelihood to the (Zermelo-)Bradley-Terry model, the most common method in statistics and psychology, is one of the ranking methods that perform best with respect to the set of properties under consideration. A less known ranking method, generalised row sum, performs well too. We also study, among others, the fair bets ranking method, widely studied in social choice, and the least squares method.

A note on NTU-convexity

Abstract. For cooperative games with transferable utility, convexity has turned out to be an important and widely applicable concept. Convexity can be defined in a number of ways, each having its own specific attractions. Basically, these definitions fall into two categories, namely those based on a supermodular interpretation and those based on a marginalistic interpretation. For games with nontransferable utility, however, the literature mainly focuses on two kinds of convexity, ordinal and cardinal convexity, which both extend the supermodular interpretation. In this paper, we analyse three types of convexity for NTU games that generalise the marginalistic interpretation of convexity.

A Composite Run-to-the-Bank Rule for Multi-Issue Allocation Situations

In this paper, we propose a new extension of the run-to-the-bank rule for bankruptcy situations to the class of multi-issue allocation situations. We show that this rule always yields a core element and that it satisfies self-duality. We characterise our rule by means of a new consistency property, issue-consistency.

The two-stage constrained equal awards and losses rules for multi-issue allocation situations

This paper considers two-stage solutions for multi-issue allocation situations, which are extensions of bankruptcy problems. Characterizations are provided for the two-stage constrained equal awards and constrained equal losses rules, based on the properties of composition up and composition down.

Drop Out Monotonic Rules for Sequencing Situations

This note introduces a new monotonicity property for sequencing situations. A sequencing rule is called drop out monotonic if no player will be worse off whenever one of the players decides to drop out of the queue before processing starts. This intuitively appealing property turns out to be very strong: we show that there is at most one rule satisfying both stability and drop out monotonicity. For the standard model of linear cost functions, the existence of this rule is established.

A geometric characterisation of the compromise value

In this paper, we characterise the compromise value of a game as the barycentre of the edges of its core cover.For this, we introduce the value, which extends the adjusted proportional rule for bankruptcy situations and coincides with the compromise value on a large class of games.

Balanced contributions for TU games with awards and applications

Abstract Calleja et al. [Calleja, P., Borm, P., Hendrickx, R., 2005. Multi-issue allocation situations. European Journal of Operational Research 164, 730–747] introduced multi-issue allocation situations with awards. In this paper, we extend the classical model of cooperative games with transferable utility to the cooperative games with transferable utility and awards. We define a run-to-the-bank rule for cooperative games with transferable utility and awards and characterise it in terms of a property of balanced contributions. We apply our main result to bankruptcy problems and multi-issue allocation situations with awards.

The Constrained Equal Awards Rule for Bankruptcy Problems with a Priori Unions

In this paper, we provide two extensions of the constrained equal awards rule for bankruptcy situations to the class of bankruptcy situations with a priori unions. We present some characterisations and relations with corresponding games. The two new extensions are illustrated by a specific application.