147 research outputs found
Solution Concepts for Games with General Coalitional Structure (Replaces CentER DP 2011-025)
We introduce a theory on marginal values and their core stability for cooperative games with arbitrary coalition structure. The theory is based on the notion of nested sets and the complex of nested sets associated to an arbitrary set system and the M-extension of a game for this set. For a set system being a building set or partition system, the corresponding complex is a polyhedral complex, and the vertices of this complex correspond to maximal strictly nested sets. To each maximal strictly nested set is associated a rooted tree. Given characteristic function, to every maximal strictly nested set a marginal value is associated to a corresponding rooted tree as in [9]. We show that the same marginal value is obtained by using the M-extension for every permutation that is associated to the rooted tree. The GC-solution is defined as the average of the marginal values over all maximal strictly nested sets. The solution can be viewed as the gravity center of the image of the vertices of the polyhedral complex. The GC-solution differs from the Myerson-kind value defined in [2] for union stable structures. The HS-solution is defined as the average of marginal values over the subclass of so-called half-space nested sets. The NT-solution is another solution and is defined as the average of marginal values over the subclass of NT-nested sets. For graphical buildings the collection of NT-nested sets corresponds to the set of spanning normal trees on the underlying graph and the NT-solution coincides with the average tree solution. We also study core stability of the solutions and show that both the HS-solution and NT-solution belong to the core under half-space supermodularity, which is a weaker condition than convexity of the game. For an arbitrary set system we show that there exists a unique minimal building set containing the set system. As solutions we take the solutions for this building covering by extending in a natural way the characteristic function to it by using its Möbius inversion.Core;polytope;building set;nested set complex;Möbius inversion;permutations;normal fan;average tree solution;Myerson value
Sequential decisions in allocation problems
In the context of cooperative TU-games, and given an order of players, we consider the problem of distributing the worth of the grand coalition as a sequential decision problem. In each step of the process, upper and lower bounds for the payoff of the players are required related to successive reduced games. Sequentially compatible payoffs are defined as those allocation vectors that meet these recursive bounds. The core of the game is reinterpreted as a set of sequentially compatible payoffs when the Davis-Maschler reduced game is considered (Th.1). Independently of the reduction, the core turns out to be the intersection of the family of the sets of sequentially compatible payoffs corresponding to the different possible orderings (Th.2), so it is in some sense order-independent. Finally, we analyze advantageous properties for the first player.core, reduced game, sequential allocation, tu-game
Stable pricing in monopoly and equilibrium-core of cost games
We prove the existence of subsidy free and sustainable pricing schedule in multiproduct contestable markets. We allow firms to discriminate the local markets that are composed by a set of the products line and a set of agents. Results are obtained under an assumption of fair sharing cost and under boundary condition of demand functions. The pricing problem is modelled in terms of equilibrium-core allocations of parameterized cost games.Cooperative games, contestable markets, sustainability, subsidy free, parameterized cost games.
Stable pricing in monopoly and equilibrium-core of cost games
URL des Cahiers : https://halshs.archives-ouvertes.fr/CAHIERS-MSECahiers de la MSE 2005.23 - SĂ©rie Bleue - ISSN : 1624-0340We prove the existence of subsidy free and sustainable pricing schedule in multiproduct contestable markets. We allow firms to discriminate the local markets that are composed by a set of the products line and a set of agents. Results are obtained under an assumption of fair sharing cost and under boundary condition of demand functions. The pricing problem is modelled in terms of equilibrium-core allocations of parameterized cost games.L'existence de tarifications sans subventions croisĂ©es et soutenable est prouvĂ©e dans un marchĂ© contestable multiproduit oĂč les firmes ont la possibilitĂ© de discriminer les marchĂ©s locaux, composĂ©s d'une partie de la ligne commerciale et d'une partie d'agents. Les rĂ©sultats sont obtenus sous une hypothĂšse de fonction de coĂ»t Ă partage Ă©quitable, et sous des conditions de bord des fonctions de demandes. Le problĂšme de tarification est modĂ©lisĂ© par des coeurs-Ă©quilibres de jeux de coĂ»t paramĂ©trĂ©s
Using Data Envelopment Analysis to Evaluate Environmentally Conscious Tourism Management
This paper discusses a methodology to assess the performances of tourism management of local governments when economic and environmental aspects are considered as equally relevant. In particular, the focus is on the comparison and efficiency assessment of Italian municipalities located on the costal areas. In order to assess the efficiency status of the considered management units, Data Envelopment Analysis (DEA), a methodology for evaluating the relative efficiency of decision making units, is applied. The efficiency index measure used in DEA analysis accounts for both environmental and economic features correlated to the tourism industry. Further, potential managerial improvements for those areas resulting far from the efficiency frontier can be investigated.Data envelopment analysis, Sustainable tourism
Herbert Scarf: a Distinguished American Economist
Herbert Eli Scarf (born on July 25, 1930 in Philadelphia, PA) is a distinguished American economist and Sterling Professor (Emeritus as of 2010) of Economics at Yale University. He is a member of the American Academy of Arts and Sciences, the National Academy of Sciences and the American Philosophical Society. He served as the president of the Econometric Society in 1983. He received both the Frederick Lanchester Award in 1973 and the John von Neumann Medal in 1983 from the Operations Research Society of America and was elected as a Distinguished Fellow of the American Economic Association in 1991.
Cost allocation in connection and conïŹict problems on networks: a cooperative game theoretic approach
This thesis examines settings where multiple decision makers with conïŹicting interests
beneïŹt from cooperation in joint combinatorial optimisation problems. It draws on cooperative game theory, polyhedral theory and graph theory to address cost sharing in
joint single-source shortest path problems and joint weighted minimum colouring problems.
The primary focus of the thesis are problems where each agent corresponds to a
vertex of an undirected complete graph, in which a special vertex represents the common supplier. The joint combinatorial optimisation problem consists of determining the
shortest paths from the supplier to all other vertices in the graph. The optimal solution
is a shortest path tree of the graph and the aim is to allocate the cost of this shortest
path tree amongst the agents. The thesis deïŹnes shortest path tree problems, proposes
allocation rules and analyses the properties of these allocation rules. It furthermore introduces shortest path tree games and studies the properties of these games. Various core
allocations for shortest path tree games are introduced and polyhedral properties of the
core are studied. Moreover, computational results on ïŹnding the core and the nucleolus
of shortest path tree games for the application of cost allocation in Wireless Multihop
Networks are presented.
The secondary focus of the thesis are problems where each agent is interested in
having access to a number of facilities but can be in conïŹict with other agents. If two
agents are in conïŹict, then they should have access to disjoint sets of facilities. The
aim is to allocate the cost of the minimum number of facilities required by the agents
amongst them. The thesis models these cost allocation problems as a class of cooperative
games called weighted minimum colouring games, and characterises total balancedness
and submodularity of this class of games using the properties of the underlying graph
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