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1.
Ignacio García-Jurado Natividad Llorca Ana Meca Manuel A. Pulido Joaquín Sánchez-Soriano 《TOP》2009,17(1):85-95
In this paper we consider finitely repeated games in which players can unilaterally commit to behave in an absentminded way
in some stages of the repeated game. We prove that the standard conditions for folk theorems can be substantially relaxed
when players are able to make this kind of compromises, both in the Nash and in the subgame perfect case. We also analyze
the relation of our model with the repeated games with unilateral commitments studied, for instance, in García-Jurado et al.
(Int. Game Theory Rev. 2:129–139, 2000).
Authors acknowledge the financial support of Ministerio de Educaci ón y Ciencia, FEDER and Fundación Séneca de la Región de Murcia through projects SEJ2005-07637-C02-02, ECO2008-03484-C02-02, MTM2005-09184-C02-02, MTM2008-06778-C02-01 and 08716/PI/08. 相似文献
2.
We introduce a new class of totally balanced cooperative TU games, namely p-additive games. It is inspired by the class of inventory games that arises from inventory situations with temporary discounts
(Toledo Ph.D. thesis, Universidad Miguel Hernández de Elche, 2002) and contains the class of inventory cost games (Meca et al. Math. Methods Oper. Res. 57:481–493, 2003). It is shown that every p-additive game and its corresponding subgames have a nonempty core. We also focus on studying the character of concave or
convex and monotone p-additive games. In addition, the modified SOC-rule is proposed as a solution for p-additive games. This solution is suitable for p-additive games, since it is a core-allocation which can be reached through a population monotonic allocation scheme. Moreover,
two characterizations of the modified SOC-rule are provided.
This work was partially supported by the Spanish Ministry of Education and Science and Generalitat Valenciana (grants MTM2005-09184-C02-02,
ACOMP06/040, CSD2006-00032). Authors acknowledge valuable comments made by the Editor and the referee. 相似文献
3.
We consider an alternative expression of the Shapley value that reveals a system of compensations: each player receives an
equal share of the worth of each coalition he belongs to, and has to compensate an equal share of the worth of any coalition
he does not belong to. We give a representation in terms of formation of the grand coalition according to an ordering of the
players and define the corresponding compensation vector. Then, we generalize this idea to cooperative games with a communication
graph in order to construct new allocation rules called the compensation solutions. Firstly, we consider cooperative games
with arbitrary graphs and construct rooted spanning trees (see Demange, J Political Econ 112:754–778, 2004) instead of orderings of the players by using the classical algorithms DFS and BFS. If the graph is complete, we show that the compensation solutions associated with DFS and BFS coincide with the Shapley value and the equal surplus division respectively. Secondly, we consider cooperative games with
a forest (cycle-free graph) and all its rooted spanning trees. The compensation solution is characterized by component efficiency
and relative fairness. The latter axiom takes into account the relative position of a player with respect to his component
in the communication graph. 相似文献
4.
M. Pulido P. Borm R. Hendrickx N. Llorca J. Sánchez-Soriano 《Annals of Operations Research》2008,158(1):133-141
This paper deals with bankruptcy situations in which in addition to the claims, an exogenously given reference point for the
allocation of the estate is present. We introduce and analyse two types of compromise solutions and show that they coincide
with the τ value of two corresponding TU games. We apply our solutions to a real-life case of allocating university money to degree
courses.
Research supported by Generalitat Valenciana, through ACOMP06/040, ACOMP07/136 and GV05/189, and by the Government of Spain
and FEDER fund under project MTM2005-09184-C02-02. M. Pulido’s research is partially supported by Fundación Séneca of Comunidad
Autónoma de la Región de Murcia, through 02911/PI/05. Ruud Hendrickx author acknowledges financial support from the Netherlands
Organisation for Scientific Research (NWO). 相似文献
5.
Luisa Carpente Balbina Casas-Méndez Ignacio García-Jurado Anne van den Nouwel 《International Journal of Game Theory》2005,33(3):397-419
In this paper we propose a new method to associate a coalitional game with each strategic game. The method is based on the lower value of finite two-player zero-sum games. We axiomatically characterize this new method, as well as the method that was described in Von Neumann and Morgenstern (1944). As an intermediate step, we provide axiomatic characterizations of the value and the lower value of matrix games and finite two-player zero-sum games, respectively.The authors acknowledge the financial support of Ministerio de Ciencia y Tecnologia, FEDER andXunta de Galicia through projects BEC2002-04102-C02-02 and PGIDIT03PXIC20701PN.We wish to thank Professor William Thomson as well as an anonymous referee for useful comments. 相似文献
6.
Harsanyi power solutions for graph-restricted games 总被引:1,自引:0,他引:1
René van den Brink Gerard van der Laan Vitaly Pruzhansky 《International Journal of Game Theory》2011,40(1):87-110
We consider cooperative transferable utility games, or simply TU-games, with limited communication structure in which players can cooperate if and only if they are connected
in the communication graph. Solutions for such graph games can be obtained by applying standard solutions to a modified or restricted game that takes account of the cooperation restrictions.
We discuss Harsanyi solutions which distribute dividends such that the dividend shares of players in a coalition are based on power measures for nodes in corresponding communication graphs. We provide axiomatic characterizations of the Harsanyi power solutions on
the class of cycle-free graph games and on the class of all graph games. Special attention is given to the Harsanyi degree
solution which equals the Shapley value on the class of complete graph games and equals the position value on the class of cycle-free graph games. The Myerson value is the Harsanyi power solution that is based on the equal power measure. Finally, various applications are discussed. 相似文献
7.
Three solution concepts for cooperative games with random payoffs are introduced. These are the marginal value, the dividend value and the selector value. Inspiration for their definitions comes from several equivalent formulations of the Shapley value for cooperative TU games. An example shows that the equivalence is not preserved since these solutions can all be different for cooperative games with random payoffs. Properties are studied and a characterization on a subclass of games is provided.2000 Mathematics Subject Classification Number: 91A12.The authors thank two anonymous referees and an associate editor for their helpful comments.This author acknowledges financial support from the Netherlands Organization for Scientific Research (NWO) through project 613-304-059.Received: October 2000 相似文献
8.
René van den Brink 《TOP》2017,25(1):1-33
In the field of cooperative games with restricted cooperation, various restrictions on coalition formation are studied. The most studied restrictions are those that arise from restricted communication and hierarchies. This survey discusses several models of hierarchy restrictions and their relation with communication restrictions. In the literature, there are results on game properties, Harsanyi dividends, core stability, and various solutions that generalize existing solutions for TU-games. In this survey, we mainly focus on axiomatizations of the Shapley value in different models of games with a hierarchically structured player set, and their applications. Not only do these axiomatizations provide insight in the Shapley value for these models, but also by considering the types of axioms that characterize the Shapley value, we learn more about different network structures. A central model of games with hierarchies is that of games with a permission structure where players in a cooperative transferable utility game are part of a permission structure in the sense that there are players that need permission from other players before they are allowed to cooperate. This permission structure is represented by a directed graph. Generalizations of this model are, for example, games on antimatroids, and games with a local permission structure. Besides discussing these generalizations, we briefly discuss some applications, in particular auction games and hierarchically structured firms. 相似文献
9.
In a transshipment game, supply chain agents cooperate to transship surplus products. Although the game has been well studied in the OR literature, the fundamental question whether the agents can afford cooperation costs to set up and maintain the game in the first place has not been addressed thus far. This paper addresses this question for the cooperative transshipment games with identical agents having normally distributed independent demands. We provide characterization of equal allocations which are in the core of symmetric games, and prove that not all transshipment games are convex. In particular, we prove that though individual allocations grow with the coalition size, the growth diminishes according to two rules of diminishing individual allocations. These results are the basis for studying the games with cooperation costs. We model the cooperation costs by the cooperation network topology and the cooperation cost per network link. We consider two network topologies, the clique and the hub, and prove bounds for the cost per link that render coalitions stable. These bounds always limit coalition size for cliques. However, the opposite is shown for hubs, namely newsvendors can afford cooperation costs only if their coalition is sufficiently large. 相似文献
10.
A core-allocation family for generalized holding cost games 总被引:2,自引:0,他引:2
Ana Meca 《Mathematical Methods of Operations Research》2007,65(3):499-517
Inventory situations, introduced in Meca et al. (Eur J Oper Res 156: 127–139, 2004), study how a collective of firms can minimize
its joint inventory cost by means of co-operation. Depending on the information revealed by the individual firms, they analyze
two related cooperative TU games: inventory cost games and holding cost games, and focus on proportional division mechanisms
to share the joint cost. In this paper we introduce a new class of inventory games: generalized holding cost games, which
extends the class of holding cost games. It turns out that generalized holding cost games are totally balanced.We then focus
on the study of a core-allocation family which is called N-rational solution family.It is proved that a particular relation of inclusion exists between the former and the core. In addition, an N-rational solution called minimum square proportional ruleis studied.
This work was partially supported by the Spanish Ministry of Education and Science, and the Generalitat Valenciana (grants
MTM2005-09184-C02-02, CSD2006-00032, ACOMP06/040). The author thanks Javier Toledo, Josefa Cá novas, and two anonymous referees
for helpful comments. 相似文献
11.
Subgame consistency is a fundamental element in the solution of cooperative stochastic differential games. In particular, it ensures that the extension of the solution policy to a later starting time and any possible state brought about by the prior optimal behavior of the players would remain optimal. Recently, mechanisms for the derivation of subgame consistent solutions in stochastic cooperative differential games with transferable payoffs have been found. In this paper, subgame consistent solutions are derived for a class of cooperative stochastic differential games with nontransferable payoffs. The previously intractable subgame consistent solution for games with nontransferable payoffs is rendered tractable.This research was supported by the Research Grant Council of Hong Kong, Grant HKBU2056/99H and by Hong Kong Baptist University, Grant FRG/02-03/II16.Communicated by G. Leitmann 相似文献
12.
We associate an optimistic TU game with each minimum cost spanning tree problem. We define the worth of a coalition S as the cost of connecting agents in S to the source assuming that agents in N\S are already connected to the source, and agents in S can connect through agents in N\S. We study the Shapley value of this new game.
We thank Hervé Moulin, William Thomson, and two referees for helpful comments. Financial support from the Ministerio de Ciencia
y Tecnologia and FEDER through grant SEJ2005-07637-c02-01 is gratefully acknowledged. 相似文献
13.
Usually, common pool games are analyzed without taking into account the cooperative features of the game, even when communication
and non-binding agreements are involved. Whereas equilibria are inefficient, negotiations may induce some cooperation and
may enhance efficiency. In the paper, we propose to use tools of cooperative game theory to advance the understanding of results
in dilemma situations that allow for communication. By doing so, we present a short review of earlier experimental evidence
given by Hackett, Schlager, and Walker 1994 (HSW) for the conditional stability of non-binding agreements established in face-to-face
multilateral negotiations. For an experimental test, we reanalyze the HSW data set in a game-theoretical analysis of cooperative
versions of social dilemma games. The results of cooperative game theory that are most important for the application are explained
and interpreted with respect to their meaning for negotiation behavior. Then, theorems are discussed that cooperative social
dilemma games are clear (alpha- and beta-values coincide) and that they are convex (it follows that the core is “large”):
The main focus is on how arguments of power and fairness can be based on the structure of the game. A second item is how fairness
and stability properties of a negotiated (non-binding) agreement can be judged. The use of cheap talk in evaluating experiments
reveals that besides the relation of non-cooperative and cooperative solutions, say of equilibria and core, the relation of
alpha-, beta- and gamma-values are of importance for the availability of attractive solutions and the stability of the such
agreements. In the special case of the HSW scenario, the game shows properties favorable for stable and efficient solutions.
Nevertheless, the realized agreements are less efficient than expected. The realized (and stable) agreements can be located
between the equilibrium, the egalitarian solution and some fairness solutions. In order to represent the extent to which the
subjects obey efficiency and fairness, we present and discuss patterns of the corresponding excess vectors. 相似文献
14.
Semivalues are solution concepts for cooperative games that assign to each player a weighted sum of his/her marginal contributions to the coalitions, where the weights only depend on the coalition size. The Shapley value and the Banzhaf value are semivalues. Mixed modified semivalues are solutions for cooperative games when we consider a priori coalition blocks in the player set. For all these solutions, a computational procedure is offered in this paper. 相似文献
15.
V. V. Rozen 《Journal of Mathematical Sciences》2018,235(6):740-755
We present a brief review of the most important concepts and results concerning games in which the goal structure is formalized by binary relations called preference relations. The main part of the work is devoted to games with ordered outcomes, i.e., game-theoretic models in which preference relations of players are given by partial orders on the set of outcomes. We discuss both antagonistic games and n-person games with ordered outcomes. Optimal solutions in games with ordered outcomes are strategies of players, situations, or outcomes of the game. In the paper, we consider noncooperative and certain cooperative solutions. Special attention is paid to an extension of the order on the set of probabilistic measures since this question is substantial for constructing the mixed extension of the game with ordered outcomes. The review covers works published from 1953 until now. 相似文献
16.
Tamás Solymosi 《Central European Journal of Operations Research》2008,16(4):425-440
Partitioning games are useful on two counts: first, in modeling situations with restricted cooperative possibilities between
the agents; second, as a general framework for many unrestricted cooperative games generated by combinatorial optimization
problems.We show that the family of partitioning games defined on a fixed basic collection is closed under the strategic equivalence
of games, and also for taking the monotonic cover of games. Based on these properties we establish the coincidence of
the Mas-Colell, the classical, the semireactive, and the reactive bargaining setswith the core for interesting balanced subclasses
of partitioning games, including assignment games, tree-restricted superadditive games, and simple network games.
Prepared during the author’s Bolyai János Research Fellowship. Also supported by OTKA grant T46194. 相似文献
17.
E. Algaba J. M. Bilbao R. van?den Brink J. J. López 《Journal of Optimization Theory and Applications》2012,155(2):650-668
In this paper, the set of feasible coalitions in a cooperative game is given by a union stable system. Well-known examples of such systems are communication situations and permission structures. Two games associated with a game on a union stable system are the restricted game (on the set of players in the game) and the conference game (on the set of supports of the system). We define two types of superfluous support property through these two games and provide new characterizations for the Myerson value. Finally, we analyze inheritance of properties between the restricted game and the conference game. 相似文献
18.
In this paper, we study cooperative games with limited cooperation possibilities, represented by a tree on the set of agents. Agents in the game can cooperate if they are connected in the tree. We introduce natural extensions of the average (rooted)-tree solution (see [Herings, P., van der Laan, G., Talman, D., 2008. The average tree solution for cycle free games. Games and Economic Behavior 62, 77–92]): the marginalist tree solutions and the random tree solutions. We provide an axiomatic characterization of each of these sets of solutions. By the way, we obtain a new characterization of the average tree solution. 相似文献
19.
In this paper we analyze cooperative games whose characteristic function takes values in a partially ordered linear space.
Thus, the classical solution concepts in cooperative game theory have to be revisited and redefined: the core concept, Shapley–Bondareva
theorem and the Shapley value are extended for this class of games. The classes of standard, vector-valued and stochastic
cooperative games among others are particular cases of this general theory.
The research of the authors is partially supported by Spanish DGICYT grant numbers MTM2004-0909, HA2003-0121, HI2003-0189,
MTM2007-67433-C02-01, P06-FQM-01366. 相似文献
20.
M. A. Mosquera I. García-Jurado M. G. Fiestras-Janeiro 《Annals of Operations Research》2008,158(1):183-188
In this note we deal with inventory games as defined in Meca et al. (Math. Methods Oper. Res. 57:483–491, 2003). In that context we introduce the property of immunity to coalitional manipulation, and demonstrate that the SOC-rule (Share the Ordering Cost) is the unique allocation rule for inventory games which satisfies
this property.
The authors acknowledge the financial support of Ministerio de Educación y Ciencia, FEDER and Xunta de Galicia through projects SEJ2005-07637-C02-02 and PGIDIT06PXIC207038PN. 相似文献