Vito Fragnelli

Game Practice and the Environment

This book summarises the latest achievements of researchers involved in the application of game theory to the analysis of environmental matters. It provides an overview of different methods and applications, and gives the reader new insights on the solutions to complex environmental problems. The authors investigate various game theoretic approaches, including cooperative and non-cooperative game theory, and analyse both dynamic and static games. They illustrate the application of these approaches to global and local environmental problems, and present novel but effective tools to support environmental policy making. In particular, they focus on three important issues; climate negotiations and policy, the sharing of environmental costs, and environmental management and pollution control.

Tree-connected peer group situations and peer group games

Abstract. A class of cooperative games arising from economic and operations research situations in which agents with potential individual possibilities are connected via a hierarchy within an organization is introduced. It is shown that the games in this class form a cone which lies in the intersection of convex games and monotonic veto-rich games with the leader of the organization as veto-player. Different economic situations like auctions, communication situations, sequencing situations and flow situations are related to peer group games. For peer group games classical solution concepts have nice computational properties.

Two Approaches to the Problem of Sharing Delay Costs in Joint Projects

This paper concentrates on cost sharing situations which arise when delayed joint projects involve joint delay costs. The problem here is to determine “fair” shares for each of the agents who contribute to the delay of the project such that the total delay cost is cleared. We focus on the evaluation of the responsibility of each agent in delaying the project based on the activity graph representation of the project and then on solving the important problem of the delay cost sharing among the agents involved. Two approaches, both rooted in cooperative game theory methods are presented as possible solutions. In the first approach delay cost sharing rules are introduced which are based on the delay of the project and on the individual delays of the agents who perform activities. This approach is inspired by the bankruptcy and taxation literature and leads to five rules: the (truncated) proportional rule, the (truncated) constrained equal reduction rule and the constrained equal contribution rule. By introducing two coalitional games related to delay cost sharing problems, which we call the pessimistic delay game and the optimistic delay game, also game theoretical solutions as the Shapley value, the nucleolus and the τ-value generate delay cost sharing rules. In the second approach the delays of the relevant paths in the activity graph together with the delay of the project play a role. A two-stage solution is proposed. The first stage can be seen as a game between paths, where the delay cost of the project has to be allocated to the paths. Here serial cost sharing methods play a role. In the second stage the allocated costs of each path are divided proportionally to the individual delays among the activities in the path.

A game theoretical approach to the classification problem in gene expression data analysis

Microarray technology allows for the evaluation of the level of expression of thousands of genes in a sample of cells under a given condition. In this paper, we introduce a methodology based on cooperative Game Theory for the selection of groups of genes with high power in classifying samples, according to gene expression patterns. The connection between microarray games and classification games is discussed and the use of the Shapley value to measure the power of genes for classification is motivated on particular instances and compared to the interaction index.

On shortest path games

Abstract. A class of cooperative TU-games arising from shortest path problems is introduced and analyzed. Some conditions under which a shortest path game is balanced are obtained. Also an axiomatic characterization of the Shapley value for this class of games is provided.

How to Share Railways Infrastructure Costs

In this paper we propose an infrastructure access tariff in a cost allocation problem arising from the reorganization of the railway sector in Europe. To that aim we introduce the class of infrastructure cost games. A game in this class is a sum of airport games and what we call maintenance cost games, and models the infrastructure costs (building and maintenance) produced when a set of different types of trains belonging to several agents makes use of a certain infrastructure. We study some properties of infrastructure cost games and provide a formula for the Shapley value of a game in this class. The access tariff we propose is based on the Shapley value of infrastructure cost games.

Sequencing Interval Situations and Related Games

In this paper we consider one-machine sequencing situations with interval data. We present different possible scenarioes and extend classical results on well known rules and on sequencing games to the interval setting.

Balanced games arising from infinite linear models

Abstract. Kalai and Zemel introduced a class of flow-games showing that these games have a non-empty core and that a minimum cut corresponds to a core allocation. We consider flow-games with a finite number of players on a network with infinitely many arcs: assuming that the total sum of the capacities is finite, we show the existence of a maximum flow and we prove that this flow can be obtained as limit of approximating flows on finite subnetworks. Similar results on the existence of core allocations and core elements are given also for minimum spanning network models (see Granot and Huberman) and semi-infinite linear production models (following the approach of Owen).

A cost allocation problem in urban solid wastes collection and disposal

Abstract.In this paper we consider a cost allocation problem arising in a consortium for urban solid wastes collection and disposal. A classical allocation rule is the proportional division according to the volume of wastes collected; here we propose a different allocation method, rooted in game theory, based on a model developed by Fragnelli et al. [3], using the Shapley Value and the Owen Value as allocation rules. The model was applied to the data of the consortium Ovadese – Valle Scrivia, comparing our results and the actual ones.

Balancedness of infrastructure cost games

Abstract In this paper we study the class of infrastructure cost games. A game in this class models the infrastructure costs (both building and maintenance) produced when a set of users of different types makes use of a certain infrastructure, which may consist of several facilities. Special attention is paid to one facility infrastructure cost games. Such games are modeled as the sum of an airport game and a maintenance cost game. It turns out that the core and nucleolus of these games are very closely related to the core and nucleolus of an associated generalized airport game. Furthermore we provide necessary and sufficient conditions under which an infrastructure cost game is balanced.