This paper focuses on two characterizations of convex interval games using the notions of superad... more This paper focuses on two characterizations of convex interval games using the notions of superadditivity and exactness, respectively. We also relate big boss interval games with concave interval games and obtain characterizations of big boss interval games in terms of subadditivity and exactness.
Supply Chain Management-an International Journal, 2005
This paper deals with cooperative fuzzy games arising from two economic situations: a linear prod... more This paper deals with cooperative fuzzy games arising from two economic situations: a linear production situation and a labor-time availability situation. In both economic situations we derive cooperative fuzzy games and study conditions for nonemptiness of Aubin's core. Also, relations between reasona-ble (stable) payoff schemes for the economic situations and core elements of the related cooperative fuzzy games are studied
This paper deals with the research area of cooperative interval games arising from airport situat... more This paper deals with the research area of cooperative interval games arising from airport situations with interval data. We also extend to airport interval games some results from classical theory.
In this paper, the egalitarian solution for convex cooperative fuzzy games is introduced. The cla... more In this paper, the egalitarian solution for convex cooperative fuzzy games is introduced. The classical Dutta -Ray algorithm for finding the constrained egalitarian solution for convex crisp games is adjusted to provide the egalitarian solution of a convex fuzzy game. For arbitrary fuzzy games, the equal division core is introduced. It turns out that both the equal division core and the egalitarian solution of a convex fuzzy game coincide with the corresponding equal division core and the constrained egalitarian solution, respectively, of the related crisp game. D
A new way is presented to define for minimum cost spanning tree (mcst) games the irreducible core... more A new way is presented to define for minimum cost spanning tree (mcst) games the irreducible core, which is introduced by Bird in 1976. The Bird core correspondence turns out to have interesting monotonicity and additivity properties and each stable cost monotonic allocation rule for mcst-problems is a selection of the Bird core correspondence. Using the additivity property an axiomatic
RODICA BRANZEI, STEFANO MORETTI, HENK NORDE and STEF TIJS THE P-VALUE FOR COST SHARING IN MINIMUM... more RODICA BRANZEI, STEFANO MORETTI, HENK NORDE and STEF TIJS THE P-VALUE FOR COST SHARING IN MINIMUM COST SPANNING TREE SITUATIONS ABSTRACT. The aim of this paper is to introduce and axiomatically characterize the P-value as a rule to solve the ...
The focus of this paper is on cooperation in compound joint projects. A group of agents aims to w... more The focus of this paper is on cooperation in compound joint projects. A group of agents aims to work together in a joint project which can have different forms. Each feasible form corresponds to a subset of a given set of basic units. The cost of the chosen project is the sum of the costs of the basic units involved
We consider the class of Obligation rules for minimum cost spanning tree situations. The main res... more We consider the class of Obligation rules for minimum cost spanning tree situations. The main result of this paper is that such rules are cost monotonic and induce also population monotonic allocation schemes. Another characteristic of Obligation rules is that they assign to a minimum cost spanning tree situation a vector of cost contributions which can be obtained as product
In this paper reasonable payoff intervals for players in a game in partition function form (p.f.f... more In this paper reasonable payoff intervals for players in a game in partition function form (p.f.f. game) are introduced and used to define the notion of compromisable p.f.f. game. For a compromisable p.f.f. game a compromise value is defined for which an axiomatic characterization is provided. Also a generic subclass of games in extensive form of perfect information without chance
This chapter examines several monotonicity properties of value-type interval solutions on the cla... more This chapter examines several monotonicity properties of value-type interval solutions on the class of convex interval games and focuses on the Dutta–Ray (DR) solution for such games. Well-known properties for the classical DR solution are extended to the interval setting. In particular, it is proved that the interval DR solution of a convex interval game belongs to the interval core
In this paper we provide some technical results related to the Lorenz dominance, which allow to p... more In this paper we provide some technical results related to the Lorenz dominance, which allow to prove that the allocation obtained by the algorithm in Dutta and Ray (1989), when exists, and the elements of the equal split-o¤ set always Lorenz dominate every allocation in the core of the game.
A class of cooperative games arising from economic and operations research situations in which ag... more 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. Di¤erent 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.
In this paper the cone of convex cooperative fuzzy games is studied. As in the classical case of ... more In this paper the cone of convex cooperative fuzzy games is studied. As in the classical case of convex crisp games, these games have a large core and the fuzzy Shapley value is the barycen- ter of the core. Surprisingly, the core and the Weber set coincide ∗ This paper was written while the authors were research fellows at the
A canonical procedure is described, which associates to each infinite information collecting situ... more A canonical procedure is described, which associates to each infinite information collecting situation a related information collecting situation with finite state and action spaces, in such a way that the two corresponding ICgames are near to each other. Compensations for informants are then also near to each other in the two IC-situations, if they are based on continuous compensation rules.
ABSTRACT In this paper, convex interval games are introduced and some characterizations are given... more ABSTRACT In this paper, convex interval games are introduced and some characterizations are given. Some economic situations leading to convex interval games are discussed. The Weber set and the Shapley value are defined for a suitable class of interval games and their relations with the interval core for convex interval games are established. A square operator is introduced which allows us to obtain interval solutions starting from classical cooperative game theory solutions. It turns out that on the class of convex interval games the square Weber set coincides with the interval core.
This paper introduces and studies a class of cooperative interval games suitable to model market ... more This paper introduces and studies a class of cooperative interval games suitable to model market situations with two corners where players face interval uncertainty regarding the outcome of cooperation. In one corner there is a powerful player called the big boss; the other corner contains players that need the big boss to benefit from cooperation. Various characterizations of big boss interval games are given. The interval core of a big boss interval game is explicitly described, bi-monotonic allocation schemes using interval core elements are introduced, and it is shown that each element of the interval core of a big boss interval game is extendable to such a scheme. Two value-type interval solution concepts are defined on the class of big boss interval games which generate for each such game the same interval core allocation which is extendable to a bi-monotonic interval allocation scheme.
... To solve such problems, we extend classical solutions from the theory of mini-mum cost spanni... more ... To solve such problems, we extend classical solutions from the theory of mini-mum cost spanning tree games. We study the properties of such solutions ... JEL Classification: C71 Key-words: cooperative cost games, minimum cost spanning tree situations, ...
This paper deals with the research area of cooperative interval games arising from airport situat... more This paper deals with the research area of cooperative interval games arising from airport situations with interval data. The major topic of the paper is to present and identify the interval Baker–Thompson rule.
This paper focuses on two characterizations of convex interval games using the notions of superad... more This paper focuses on two characterizations of convex interval games using the notions of superadditivity and exactness, respectively. We also relate big boss interval games with concave interval games and obtain characterizations of big boss interval games in terms of subadditivity and exactness.
Supply Chain Management-an International Journal, 2005
This paper deals with cooperative fuzzy games arising from two economic situations: a linear prod... more This paper deals with cooperative fuzzy games arising from two economic situations: a linear production situation and a labor-time availability situation. In both economic situations we derive cooperative fuzzy games and study conditions for nonemptiness of Aubin's core. Also, relations between reasona-ble (stable) payoff schemes for the economic situations and core elements of the related cooperative fuzzy games are studied
This paper deals with the research area of cooperative interval games arising from airport situat... more This paper deals with the research area of cooperative interval games arising from airport situations with interval data. We also extend to airport interval games some results from classical theory.
In this paper, the egalitarian solution for convex cooperative fuzzy games is introduced. The cla... more In this paper, the egalitarian solution for convex cooperative fuzzy games is introduced. The classical Dutta -Ray algorithm for finding the constrained egalitarian solution for convex crisp games is adjusted to provide the egalitarian solution of a convex fuzzy game. For arbitrary fuzzy games, the equal division core is introduced. It turns out that both the equal division core and the egalitarian solution of a convex fuzzy game coincide with the corresponding equal division core and the constrained egalitarian solution, respectively, of the related crisp game. D
A new way is presented to define for minimum cost spanning tree (mcst) games the irreducible core... more A new way is presented to define for minimum cost spanning tree (mcst) games the irreducible core, which is introduced by Bird in 1976. The Bird core correspondence turns out to have interesting monotonicity and additivity properties and each stable cost monotonic allocation rule for mcst-problems is a selection of the Bird core correspondence. Using the additivity property an axiomatic
RODICA BRANZEI, STEFANO MORETTI, HENK NORDE and STEF TIJS THE P-VALUE FOR COST SHARING IN MINIMUM... more RODICA BRANZEI, STEFANO MORETTI, HENK NORDE and STEF TIJS THE P-VALUE FOR COST SHARING IN MINIMUM COST SPANNING TREE SITUATIONS ABSTRACT. The aim of this paper is to introduce and axiomatically characterize the P-value as a rule to solve the ...
The focus of this paper is on cooperation in compound joint projects. A group of agents aims to w... more The focus of this paper is on cooperation in compound joint projects. A group of agents aims to work together in a joint project which can have different forms. Each feasible form corresponds to a subset of a given set of basic units. The cost of the chosen project is the sum of the costs of the basic units involved
We consider the class of Obligation rules for minimum cost spanning tree situations. The main res... more We consider the class of Obligation rules for minimum cost spanning tree situations. The main result of this paper is that such rules are cost monotonic and induce also population monotonic allocation schemes. Another characteristic of Obligation rules is that they assign to a minimum cost spanning tree situation a vector of cost contributions which can be obtained as product
In this paper reasonable payoff intervals for players in a game in partition function form (p.f.f... more In this paper reasonable payoff intervals for players in a game in partition function form (p.f.f. game) are introduced and used to define the notion of compromisable p.f.f. game. For a compromisable p.f.f. game a compromise value is defined for which an axiomatic characterization is provided. Also a generic subclass of games in extensive form of perfect information without chance
This chapter examines several monotonicity properties of value-type interval solutions on the cla... more This chapter examines several monotonicity properties of value-type interval solutions on the class of convex interval games and focuses on the Dutta–Ray (DR) solution for such games. Well-known properties for the classical DR solution are extended to the interval setting. In particular, it is proved that the interval DR solution of a convex interval game belongs to the interval core
In this paper we provide some technical results related to the Lorenz dominance, which allow to p... more In this paper we provide some technical results related to the Lorenz dominance, which allow to prove that the allocation obtained by the algorithm in Dutta and Ray (1989), when exists, and the elements of the equal split-o¤ set always Lorenz dominate every allocation in the core of the game.
A class of cooperative games arising from economic and operations research situations in which ag... more 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. Di¤erent 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.
In this paper the cone of convex cooperative fuzzy games is studied. As in the classical case of ... more In this paper the cone of convex cooperative fuzzy games is studied. As in the classical case of convex crisp games, these games have a large core and the fuzzy Shapley value is the barycen- ter of the core. Surprisingly, the core and the Weber set coincide ∗ This paper was written while the authors were research fellows at the
A canonical procedure is described, which associates to each infinite information collecting situ... more A canonical procedure is described, which associates to each infinite information collecting situation a related information collecting situation with finite state and action spaces, in such a way that the two corresponding ICgames are near to each other. Compensations for informants are then also near to each other in the two IC-situations, if they are based on continuous compensation rules.
ABSTRACT In this paper, convex interval games are introduced and some characterizations are given... more ABSTRACT In this paper, convex interval games are introduced and some characterizations are given. Some economic situations leading to convex interval games are discussed. The Weber set and the Shapley value are defined for a suitable class of interval games and their relations with the interval core for convex interval games are established. A square operator is introduced which allows us to obtain interval solutions starting from classical cooperative game theory solutions. It turns out that on the class of convex interval games the square Weber set coincides with the interval core.
This paper introduces and studies a class of cooperative interval games suitable to model market ... more This paper introduces and studies a class of cooperative interval games suitable to model market situations with two corners where players face interval uncertainty regarding the outcome of cooperation. In one corner there is a powerful player called the big boss; the other corner contains players that need the big boss to benefit from cooperation. Various characterizations of big boss interval games are given. The interval core of a big boss interval game is explicitly described, bi-monotonic allocation schemes using interval core elements are introduced, and it is shown that each element of the interval core of a big boss interval game is extendable to such a scheme. Two value-type interval solution concepts are defined on the class of big boss interval games which generate for each such game the same interval core allocation which is extendable to a bi-monotonic interval allocation scheme.
... To solve such problems, we extend classical solutions from the theory of mini-mum cost spanni... more ... To solve such problems, we extend classical solutions from the theory of mini-mum cost spanning tree games. We study the properties of such solutions ... JEL Classification: C71 Key-words: cooperative cost games, minimum cost spanning tree situations, ...
This paper deals with the research area of cooperative interval games arising from airport situat... more This paper deals with the research area of cooperative interval games arising from airport situations with interval data. The major topic of the paper is to present and identify the interval Baker–Thompson rule.
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