Search Results (8)

There is a long tradition of studying river sharing problems. A central question frequently examined and addressed is how common benefits or costs can be distributed fairly. In this context, axiomatic approaches of cooperative game theory often use contradictory principles of international water law, which are strictly rejected in practice. That leads to the question: Are these methods suitable for a real-world application? First, we conduct a systematic literature review based on the PRISMA approach to categorise the river sharing problems. We identified several articles describing a variety of methods and real-world applications, highlighting interdisciplinary interest. Second, we evaluate the identified axiomatic literature related to TU games with regard to their suitability for real-world applications. We exclude those “standalone” methods that exclusively follow extreme principles and/or do not describe cooperative behaviour. This is essential for a fair distribution. Third, we propose to use the traditional game-theoretical approach of airport games in the context of river protection measures to ensure a better economic interpretation and to enforce future cooperation in the joint implementation of protective measures. Full article

We introduce a new network centrality measure founded on the Gately value for cooperative games with transferable utilities. A directed network is interpreted as representing control or authority relations between players—constituting a hierarchical network. The power distribution embedded within a hierarchical network can be represented through appropriate TU-games. We investigate the properties of these TU-representations and investigate the Gately value of the TU-representation resulting in the Gately power measure. We establish when the Gately measure is a core power gauge, investigate the relationship of the Gately with the $\beta$-measure, and construct an axiomatisation of the Gately measure. Full article

In this paper, we propose a characteristic function of the maxmax defensive-equilibrium representation that maps every TU-game with strategies to a TU-game. This characteristic function is given by a two-step procedure in which each of any two complementary coalitions successively selects the equilibrium in a way that maximizes its utility. We then investigate the properties of this characteristic function and present the relations of the cores under three characteristic functions. Finally, as applications of our findings, we provide a firm production advertising game, a supply chain network game, a cost game with strategies, and a Cournot game. Full article

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A solution for TU-games assigns a set of payoff distributions to every TU-game. In the literature, various models of games with restricted cooperation can be found where, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper, we consider games on a union-closed system where the set of feasible coalitions is closed under the union, i.e., for any two feasible coalitions also, their union is feasible. Properties of solutions (the core, the nucleolus, and the prekernel) are discussed for games on a union-closed system. Full article

In a non-negative profit game that possesses a Population Monotonic Allocation Scheme (PMAS), being a member of a larger coalition implies that your profit cannot decrease. In this paper, we refer to such games as PMAS profit games. As population monotonicity is a nice and desirable property that encourages formation of larger coalitions and implies stability of the grand coalition, we explore if this special feature of PMAS games can help in identifying additional stable coalition structures under different stability concepts in cooperative games—namely, core partitions, the von Neumann–Morgenstern (vNM) stable set, the largest consistent set, and the equilibrium process of coalition formation (EPCF)—and in developing relationships between coalition structures that are stable under these different stability concepts. We first define two special classes of players for PMAS profit games—extreme and strong players—and use them to develop an algorithm for construction of stable (core) partitions. We also use extreme players to identify absorbing states for equilibrium processes of coalition formation with high level of farsightedness. We then explore the impact of population monotonicity on the relationship between stable coalition structures under abovementioned stability concepts. While we are able to obtain some results related to stability of the grand coalition and to establish relationships between stable coalition structures under different stability notions that are consistent with the existing body of knowledge, population monotonicity in general does not add enough for strengthening of the existing results. However, we are able to show a couple of more general result that hold for arbitrary cooperative TU profit games. That is, we show that the members of vNM farsighted stable sets are core partitions, and that core partitions are members of a vNM stable sets. Moreover, we show that the members of vNM farsighted stable sets are EPCF-stable partitions. Full article

In this paper, we define a family of values for directed communication situations that are inspired by the position value. We use the concept of directed communication and related connectedness in directed graphs, under which a coalition of players in a game can only cooperate if these players form a directed path in a directed communication graph. By defining an arc game, which assesses the worth of coalitions of (directed) arcs in generating worth, we allocate the Shapley value payoff of each arc over the nodes incident with this arc, where we allow the head and tail to obtain a different share in this arc payoff. However, the way that the arc payoff is shared over its head and tail is uniform over all arcs. We characterize these values by connection efficiency and a modification of the classical balanced link contributions property for undirected communication situations, discriminating between the roles of the nodes as head and tail. Full article

Green agriculture can improve biodiversity, increase farmers’ income, reduce agricultural non-point source pollution, solve food safety issues, and will be an important way to promote sustainable development in China. At present, the green transformation of China’s agriculture has encountered a bottleneck in the development of a green agricultural product market. How to develop a green agricultural product market has become an issue worthy of in-depth study in the academia. Previous studies have already given persuasive explanations for the inability to form a green agricultural product market, but few have explored its development path from the angle of cooperation. By employing the method of a Transferable Utilities (TU) cooperative game, and based on theoretical analyses and hypothetical data, this thesis aims to prove the effectiveness of the multilateral coalition to develop the green agricultural product market in China. The results show the effectiveness of the developed model of the green agricultural product market in which producers, consumers, food safety inspection departments, and e-commerce platforms cooperate with each other. This model meets the objective needs of the times and that of the market economy. According to the marginal contribution value of participants in different coalition orders, this thesis finds 6 kinds of coalition orders. When producers and consumers of green agricultural products enter the coalition in the last place, the marginal contribution value is maximized, which reflects the importance of the supply side and demand side of green agricultural products. In other words, the development of the green agricultural product market is a dynamic process—determined by consumers and promoted by producers—in which both sides promote and restrict each other. Finally, this article presents two policy recommendations: at the national level, to clearly proposes a strategy to build a green agricultural product e-commerce platform in China and to launch a pilot application for the specialized e-commerce platform for green agricultural products in the Guizhou province. Full article

A generalization of transferable utility cooperative games from the functional forms introduced by von Neumann and Morgenstern (1944, Theory of Games and Economic Behavior) and Lucas and Thrall (1963, Naval Research Logistics Quarterly, 10, 281–298) is proposed to allow for multiple membership. The definition of the core is adapted analogously and the possibilities for the cross-cutting of contractual arrangements are illustrated and discussed. Full article