Fioravante Patrone

Cooperative Game Theory and its Application to Natural, Environmental, and Water Resource Issues: 3. Application to Water Resources

This paper reviews various applications of cooperative game theory (CGT) to issues of water resources. With an increase in the competition over various water resources, the incidents of disputes have been in the center of allocation agreements. The paper reviews the cases of various water uses, such as multi-objective water projects, irrigation, groundwater, hydropower, urban water supply, wastewater, and transboundary water disputes. In addition to providing examples of cooperative solutions to allocation problems, the conclusion from this review suggests that cooperation over scarce water resources is possible under a variety of physical conditions and institutional arrangements. In particular, the various approaches for cost sharing and for allocation of physical water infrastructure and flow can serve as a basis for stable and efficient agreement, such that long-term investments in water projects are profitable and sustainable. The latter point is especially important, given recent developments in water policy in various countries and regional institutions such as the European Union (Water Framework Directive), calling for full cost recovery of investments and operation and maintenance in water projects. The CGT approaches discussed and demonstrated in this paper can provide a solid basis for finding possible and stable cost-sharing arrangements.

Game practice : contributions from applied game theory

Preface. 1. Some Tips Concerning Application of Game Theory to Real Problems M. Maschler. 2. Game Theory as a Tool for Market Design A.E. Roth. 3. On the Exploitation of Casino Games: How to Distinguish Between Games of Chance and Games of Skill? P. Borm, B. van der Genutgen. 4. Agreement Through Threats: The Northern Ireland Case S.J. Brams, J.M. Togman. 5. The Dutch DCS-1800 Auction E. van Damme. 6. Birds Tree Allocations Revisited V. Feltkamp, et al. 7. How to Share Railways Infrastructure Costs? V. Fragnelli, et al. 8. Why punish? Norms and Revenge in an Experimental Game U. Gneezy, A. Stoler. 9. A Game-Theoretical Perspective for the Detection of Tacit Collusion M. Grillo. 10. Structural Estimation of Auction Models H. Hong, M. Shum. 11. A Multiplicative Variant of the Shapley Value for Factorizing the Risk of Disease M. Land, O. Gefeller. 12. Experiments on Auctions with Random Prizes and EU/non-EU Bidders L. Parisio. 13. Dynamic Games and Oligopoly Models of Technological Innovation. 14. The Structure of Fair-Division Problems and the Design of Fair-Negotiation Procedures M.G. Raith. 15. Effectivity Functions and Parliamentary Governance Structures S. Vannucci. 16. Sequential Production Situations and Potentials M. Voorneveld, et al. 17. Approximate Envy-Fee Procedures D.-Z. Zeng. Index.

Combining Shapley value and statistics to the analysis of gene expression data in children exposed to air pollution

BackgroundIn gene expression analysis, statistical tests for differential gene expression provide lists of candidate genes having, individually, a sufficiently low p-value. However, the interpretation of each single p-value within complex systems involving several interacting genes is problematic. In parallel, in the last sixty years, game theory has been applied to political and social problems to assess the power of interacting agents in forcing a decision and, more recently, to represent the relevance of genes in response to certain conditions.ResultsIn this paper we introduce a Bootstrap procedure to test the null hypothesis that each gene has the same relevance between two conditions, where the relevance is represented by the Shapley value of a particular coalitional game defined on a microarray data-set. This method, which is called Comparative Analysis of Shapley value (shortly, CASh), is applied to data concerning the gene expression in children differentially exposed to air pollution. The results provided by CASh are compared with the results from a parametric statistical test for testing differential gene expression. Both lists of genes provided by CASh and t-test are informative enough to discriminate exposed subjects on the basis of their gene expression profiles. While many genes are selected in common by CASh and the parametric test, it turns out that the biological interpretation of the differences between these two selections is more interesting, suggesting a different interpretation of the main biological pathways in gene expression regulation for exposed individuals. A simulation study suggests that CASh offers more power than t-test for the detection of differential gene expression variability.ConclusionCASh is successfully applied to gene expression analysis of a data-set where the joint expression behavior of genes may be critical to characterize the expression response to air pollution. We demonstrate a synergistic effect between coalitional games and statistics that resulted in a selection of genes with a potential impact in the regulation of complex pathways.

Cooperative Game Theory and its Application to Natural, Environmental, and Water Resource Issues: 2. Application to Natural and Environmental Resources

This paper provides a review of various applications of cooperative game theory (CGT) to issues of natural and environmental resources. With an increase in the level of competition over environmental and natural resources, the incidents of disputes have been at the center of allocation agreements. The paper reviews the cases of common pool resources such as fisheries and forests, and cases of environmental pollution such as acid rain, flow, and stock pollution. In addition to providing examples of cooperative solutions to allocation problems, the conclusion from this review suggests that cooperation over scarce environmental and natural resources is possible under a variety of physical conditions and institutional arrangements. CGT applications to international fishery disputes are especially useful in that they have been making headway in policy-related agreements among states and regions of the world. Forest applications are more local in nature, but of great relevance in solving disputes among communities and various levels of governments.

The Shapley and Banzhaf values in microarray games

We provide a characterization of the Banzhaf value on the class of the microarray games, and another characterization of the Shapley value, on the same class, in the spirit of [Moretti S, Patrone F, Bonassi S. The class of microarray games and the relevance index for genes. TOP 2007;15:256-80]. Then we compare the results given by the two indices when applied to a colon tumor data-set published in literature.

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.

Cooperative Game Theory and its Application to Natural, Environmental, and Water Resource Issues: 1. Basic Theory

Game theory provides useful insights into the way parties that share a scarce resource may plan their use of the resource under different situations. This review provides a brief and self-contained introduction to the theory of cooperative games. It can be used to get acquainted with the basics of cooperative games. Its goal is also to provide a basic introduction to this theory, in connection with a couple of surveys that analyze its use in the context of environmental problems and models. The main models (bargaining games, transfer utility, and non-transfer utility games) and issues and solutions are considered: bargaining solutions, single-value solutions like the Shapley value and the nucleolus, and multi-value solutions such as the core. The cooperative game theory (CGT) models that are reviewed in this paper favor solutions that include all possible players and ignore the strategic stages leading to coalition building. They focus on the possible results of the cooperation by answering questions such as: Which coalitions can be formed? And how can the coalitional gains be divided to secure a sustainable agreement? An important aspect associated with the solution concepts of CGT is the equitable and fair sharing of the cooperation gains.

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).

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.

Application of Stochastic Cooperative Games in Water Resources

Traditionally, cooperative game theory has been applied to a variety of water resource problems assuming a deterministic pattern of supply. On the other hand, in view of the important role that water plays in regional and local projects, and taking into account that with climate change affecting the water cycle, the world is expected to face more stochastic and extreme events of water supply, incorporating stochastic consideration of water supply becomes more acute in designing water facilities. Moreover, various water users may have different attitudes toward risk, depending on their economic, managerial, and institutional capacity. Therefore, the combination of stochastic events and players’ risk attitude become increasingly an important issue in designing water related economic activities that depend on cooperation among the users. In this paper we will apply a Stochastic GT framework, based on the work of Suijs and Borm (1996). We will use an example of a water treatment plant to illustrate the approach, although the principles hold also for cases of other water-related joint cost, such as for storage, etc. Our goal will be to offer, in the most simplified setting, some instances of problems which appear whenever one tries to take into account the stochastic aspects of the problem which is being modelled.