- Tilburg, North Brabant, Netherlands
hans reijnierse
Tilburg University, Eor, Department Member
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This paper introduces yet another algorithm to compute the nucleolus of a standard tree game. One advantage of this algorithm is that it provides a very intuitive interpretation of the nucleolus, under which the players participate in a... more
This paper introduces yet another algorithm to compute the nucleolus of a standard tree game. One advantage of this algorithm is that it provides a very intuitive interpretation of the nucleolus, under which the players participate in a joint enterprize in which each group sends a member to help the community. Another advantage is that it demonstrates monotonicity properties of the nucleolus within this class of games. As a consequence the nucleolus of a tree game can be extended to a population monotonic allocation scheme.
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A new bargaining set based on notions of both internal and external stability is developed in the context of endogenous coalition formation. It allows one to make an explicit distinction between within-group and outside-group deviation... more
A new bargaining set based on notions of both internal and external stability is developed in the context of endogenous coalition formation. It allows one to make an explicit distinction between within-group and outside-group deviation options. This type of distinction is not present in current bargaining sets. For the class of monotonic proper simple games, the outcomes in the bargaining set are characterized. Furthermore, it is shown that the bargaining set of any homogeneous weighted majority game contains an outcome for which the underlying coalition structure consists of a minimal winning coalition and its complement.
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In labor market models as well as in exchange economies with indivisible goods gross substitutability is used as a property to guarantee the existence of competitive equilibria. This paper develops an easy way to check gross... more
In labor market models as well as in exchange economies with indivisible goods gross substitutability is used as a property to guarantee the existence of competitive equilibria. This paper develops an easy way to check gross substitutability for utility functions concerning a finite set of indivisible goods (or employees) and money. Concavity is one of the conditions that has to be satisfied. Only one other, but similar, type of relation must be checked to guarantee gross substitutability.
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This article analyses congestion in network situations from a cooperative game theoretic perspective. In network situations, players have to connect themselves to a source. As we consider publicly available networks, any group of players... more
This article analyses congestion in network situations from a cooperative game theoretic perspective. In network situations, players have to connect themselves to a source. As we consider publicly available networks, any group of players is allowed to use the entire network to establish their connections. We deal with the problem of finding an optimal network and discuss the associated cost allocation problem. For the latter, we introduce two different transferable utility cost games. For concave cost functions, we use the direct cost game, in which coalition costs are based on what a coalition can do in the absence of other players. This article, however, mainly discusses network situations with convex cost functions, which are analyzed by the use of the marginal cost game. In this game, the cost of a coalition is defined as the additional cost it induces when it joins the complementary group of players. We prove that this game is concave. Furthermore, we define a cost allocation by means of three equal treatment principles and show that this allocation is an element of the core of the marginal cost game. These results are extended to a class of continuous network situations and associated games. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010
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. For a collection Ω of subsets of a finite set N we define its core to be equal to the polyhedral cone {x∈IR N : ∑ i∈N x i =0 and ∑ i∈S x i ≥0 for all S∈Ω}. This note describes several applications of this concept in the field of... more
. For a collection Ω of subsets of a finite set N we define its core to be equal to the polyhedral cone {x∈IR N : ∑ i∈N x i =0 and ∑ i∈S x i ≥0 for all S∈Ω}. This note describes several applications of this concept in the field of cooperative game theory. Especially collections Ω are considered with core equal to {0}. This property of a one-point core is proved to be equivalent to the non-degeneracy and balancedness of Ω. Further, the notion of exact cover is discussed and used in a second characterization of collections Ω with core equal to {0}.
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In this paper we show that already relatively small collections of coalitions determine the nucleolus of a TU-game. We also show that for certain classes of combinatorial games a rather small collection of coalitions that determine the... more
In this paper we show that already relatively small collections of coalitions determine the nucleolus of a TU-game. We also show that for certain classes of combinatorial games a rather small collection of coalitions that determine the nucleolus can be givenbeforehand, i.e., without knowing the nucleolus.Journal of Economic LiteratureClassification Number: C71.
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The class of games for which the core coincides with the core cover (compromise stable games) is characterized. Moreover, an easy explicit formula for the nucleolus of this class of games is developed, using an approach based on... more
The class of games for which the core coincides with the core cover (compromise stable games) is characterized. Moreover, an easy explicit formula for the nucleolus of this class of games is developed, using an approach based on bankruptcy problems. Also, the class of convex and compromise stable games is characterized. The relation between the core cover and the Weber set is studied and it is proved that under a weak condition their intersection is nonempty.
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This paper introduces processing problems with shared interest as an extension of processing situations with restricted capacities (Meertens, M., et al., Processing games with restricted capacities, 2004). Next to an individual capacity... more
This paper introduces processing problems with shared interest as an extension of processing situations with restricted capacities (Meertens, M., et al., Processing games with restricted capacities, 2004). Next to an individual capacity to handle jobs, each player now may have interest in the completion of more than one job, and the degrees of interest may vary among players. By cooperating the players can bundle their capacities and follow an optimal processing scheme to minimize total joint costs. The resulting cost allocation problem is analyzed by considering an associated cooperative cost game. An explicit core allocation of this game is provided.
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We extend the consistency principle for strategic games (Peleg and Tijs (1996)) to apply to solutions which assign to each game a collection of product sets of strategies. Such solutions turn out to satisfy desirable properties that... more
We extend the consistency principle for strategic games (Peleg and Tijs (1996)) to apply to solutions which assign to each game a collection of product sets of strategies. Such solutions turn out to satisfy desirable properties that solutions assigning to each game a collection of strategy profiles lack. Our findings lead us to propose a new direction for normative game theory.
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This paper analyzes the compromise social choice correspondence derived from the τ-value of digraph games. Monotonicity of this correspondence is shown. A connection between several properties of social choice correspondences based on... more
This paper analyzes the compromise social choice correspondence derived from the τ-value of digraph games. Monotonicity of this correspondence is shown. A connection between several properties of social choice correspondences based on game theoretical solutions and game theoretical properties of the underlying solutions is given. Applications to several game theoretic solutions are provided.
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According to Maschler, Peleg and Shapley (1972) the bargaining set of aconvex game coincides with its core and the kernel consists of the nucleolus only. In this paper we prove the same properties for Γ-component additive games (=graph... more
According to Maschler, Peleg and Shapley (1972) the bargaining set of aconvex game coincides with its core and the kernel consists of the nucleolus only. In this paper we prove the same properties for Γ-component additive games (=graph restricted games in the sense of Owen (1986)) if Γ is a tree. Furthermore, we give a description of the nucleolus of this type of games which makes it easier accessible for computation
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A balanced set of weights infers an inequality that games with a nonempty coreobey. This paper gives a generalization of the notion `balanced set of weights".Herewith it provides necessary and su#cient conditions to determine... more
A balanced set of weights infers an inequality that games with a nonempty coreobey. This paper gives a generalization of the notion `balanced set of weights".Herewith it provides necessary and su#cient conditions to determine whether aTU-game has a population monotonic allocation scheme or not.Furthermore it shows that every 4-person integer valued game with a populationmonotonic allocation scheme has an integer
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Digraph games are cooperative TU-games associated to digraph competitions: domination structures that can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to... more
Digraph games are cooperative TU-games associated to digraph competitions: domination structures that can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles for a group of individuals within the framework of social choice theory. Brink and Gilles (2000) defined theβ-measure of a digraph competition as the Shapley value of the corresponding digraph game. This paper provides a new characterization of theβ-measure.
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This paper investigates the existence of envy-free and Pareto efficient allocations in economies with finitely many indivisible goods and one divisible good (money). The existence of envy-free allocations is proved under very weak... more
This paper investigates the existence of envy-free and Pareto efficient allocations in economies with finitely many indivisible goods and one divisible good (money). The existence of envy-free allocations is proved under very weak conditions, but the paper contains an example of an economy in which the set of envy-free allocations and the set of Pareto efficient allocations are disjoint. It contains moreover sufficient conditions for an economy in which the existence of an envy-free and Pareto efficient allocation is assured.
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The problem of financing a set of discrete public goods (facilities, projects) by private contributions is studied. The corresponding cooperative game, the realization game, is shown to be convex. For the noncooperative setting we study a... more
The problem of financing a set of discrete public goods (facilities, projects) by private contributions is studied. The corresponding cooperative game, the realization game, is shown to be convex. For the noncooperative setting we study a realization scheme that induces a strategic game. This contribution game is shown to be a generalized ordinal potential game; a best-response in the contribution
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Traveling salesman problems with revenues form a generalization of traveling salesman problems. Here, next to travel costs an explicit revenue is generated by visiting a city. We analyze routing problems with revenues, where a... more
Traveling salesman problems with revenues form a generalization of traveling salesman problems. Here, next to travel costs an explicit revenue is generated by visiting a city. We analyze routing problems with revenues, where a predetermined route on all cities determines the tours along subgroups. Corresponding routing games with revenues are analyzed. It is shown that these games have a nonempty core and a complete description of the core is provided.
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Informationally robust equilibria (IRE) are introduced in Robson (Games Econ Behav 7: 233–245, 1994) as a refinement of Nash equilibria for strategic games. Such equilibria are limits of a sequence of (subgame perfect) Nash equilibria in... more
Informationally robust equilibria (IRE) are introduced in Robson (Games Econ Behav 7: 233–245, 1994) as a refinement of Nash equilibria for strategic games. Such equilibria are limits of a sequence of (subgame perfect) Nash equilibria in perturbed games where with small probability information about the strategic behavior is revealed to other players (information leakage). Focusing on bimatrix games, we consider a type of informationally robust equilibria and derive a number of properties they form a non-empty and closed subset of the Nash equilibria. Moreover, IRE is a strict concept in the sense that the IRE are independent of the exact sequence of probabilities with which information is leaked. The set of IRE, like the set of Nash equilibria, is the finite union of polytopes. In potential games, there is an IRE in pure strategies. In zero-sum games, the set of IRE has a product structure and its elements can be computed efficiently by using linear programming. We also discuss extensions to games with infinite strategy spaces and more than two players.