共查询到20条相似文献,搜索用时 15 毫秒
1.
Shiran Rachmilevitch 《International Journal of Game Theory》2011,40(1):63-85
We provide new characterizations of the egalitarian bargaining solution on the class of strictly comprehensive n-person bargaining problems. The main axioms used in all of our results are Nash’s IIA and disagreement point monotonicity—an
axiom which requires a player’s payoff to strictly increase in his disagreement payoff. For n = 2 these axioms, together with other standard requirements, uniquely characterize the egalitarian solution. For n > 2 we provide two extensions of our 2-person result, each of which is obtained by imposing an additional axiom on the solution.
Dropping the axiom of anonymity, strengthening disagreement point monotonicity by requiring player i’s payoff to be a strictly decreasing function of the disagreement payoff of every other player j ≠ i, and adding a “weak convexity” axiom regarding changes of the disagreement point, we obtain a characterization of the class
of weighted egalitarian solutions. This “weak convexity” axiom requires that a movement of the disagreement point in the direction
of the solution point should not change the solution point. We also discuss the so-called “transfer paradox” and relate it
to this axiom. 相似文献
2.
If a player is removed from a game, what keeps the payoff of the remaining players unchanged? Is it the removal of a special player or its presence among the remaining players? This article answers this question in a complement study to Kamijo and Kongo (2012). We introduce axioms of invariance from player deletion in presence of a special player. In particular, if the special player is a nullifying player (resp. dummifying player), then the equal division value (resp. equal surplus division value) is characterized by the associated axiom of invariance plus efficiency and balanced cycle contributions. There is no type of special player from such a combination of axioms that characterizes the Shapley value. 相似文献
3.
C. Manuel E. González-Arangüena R. van den Brink 《Mathematical Methods of Operations Research》2013,77(1):1-14
In this paper we provide new axiomatizations of the Shapley value for TU-games using axioms that are based on relational aspects in the interactions among players. Some of these relational aspects, in particular the economic or social interest of each player in cooperating with each other, can be found embedded in the characteristic function. We define a particular relation among the players that it is based on mutual indifference. The first new axiom expresses that the payoffs of two players who are not indifferent to each other are affected in the same way if they become enemies and do not cooperate with each other anymore. The second new axiom expresses that the payoff of a player is not affected if players to whom it is indifferent leave the game. We show that the Shapley value is characterized by these two axioms together with the well-known efficiency axiom. Further, we show that another axiomatization of the Shapley value is obtained if we replace the second axiom and efficiency by the axiom which applies the efficiency condition to every class of indifferent players. Finally, we extend the previous results to the case of weighted Shapley values. 相似文献
4.
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
5.
In this paper, we propose a new kind of players as a compromise between the null player and the A-null player. It turns out that the axiom requiring this kind of players to get zero-payoff together with the well-known axioms of efficiency, additivity, coalitional symmetry, and intra-coalitional symmetry characterize the Shapley–solidarity value. This way, the difference between the Shapely–solidarity value and the Owen value is pinpointed to just one axiom. 相似文献
6.
Many axiomatic characterizations of values for cooperative games invoke axioms which evaluate the consequences of removing an arbitrary player. Balanced contributions (Myerson, 1980) and balanced cycle contributions (Kamijo and Kongo, 2010) are two well-known examples of such axioms. We revisit these characterizations by nullifying a player instead of deleting her/him from a game. The nullification (Béal et al., 2014a) of a player is obtained by transforming a game into a new one in which this player is a null player, i.e. the worth of the coalitions containing this player is now identical to that of the same coalition without this player. The degree with which our results are close to the original results in the literature is connected to the fact that the targeted value satisfies the null player out axiom (Derks and Haller, 1999). We also revisit the potential approach (Hart and Mas-Colell, 1989) similarly. 相似文献
7.
8.
Yan-An Hwang 《International Journal of Game Theory》2009,38(3):305-324
The paper follows Kalai and Samet’s (Econometrica 53:307–327, 1985) construction to define a possible extension of the equal allocation of nonseparable costs (EANSC) to games without transferable utilities. We offer a characterization of the EANSC based on the axiom of independence of irrelevant monotonic transformation [Chang and Hwang (Int J Game Theory 32:253–271, 2003) introduced this axiom, and they named it independence of irrelevant
expansions. The referee points out that the terminology is inappropriate. So, we change the name.] introduced by Chang and
Hwang (Int J Game Theory 32:253–271, 2003) as well as on several familiar axioms. Specifically, we show that the EANSC is
the only solution to satisfy Pareto optimality, translation covariance, anonymity, TU-bilateral consistency (or TU-converse consistency), aggregate monotonicity, and independence of irrelevant monotonic transformation. 相似文献
9.
Nicolas Houy 《Mathematical Social Sciences》2011,61(3):166-169
We characterize choice correspondences that can be rationalized by a procedure that is a refinement of the prudent choices exposed in (Houy, 2010). Our characterization is made by means of the usual expansion axiom γ and a weakening of the usual contraction axiom α. We also make a link with traditional rationality. 相似文献
10.
This paper introduces and analyzes the class of inequality averse multi-utilitarian solutions for cooperative bargaining problems.
We show that generalized Gini solutions and inequality averse Choquet solutions are particular cases of this new multi-valued
solution concept and provide a complete characterization in which an invariance property, consisting of a weakening of both
the linear invariance axiom in Blackorby et al. (Econometrica 62:1161–1178, 1994) and the restricted invariance axiom in Ok
and Zhou (Games Econ Behav 33:249–264, 2000), plays an important role. Moreover, by relaxing the assumptions involved in the
characterization, the class is extended to include inequality loving multi-utilitarian solutions which are also studied in
the paper. 相似文献
11.
Christophe Labreuche 《European Journal of Operational Research》2011,214(1):99-108
The notion of interaction among a set of players has been defined on the Boolean lattice and Cartesian products of lattices. The aim of this paper is to extend this concept to combinatorial structures with forbidden coalitions. The set of feasible coalitions is supposed to fulfil some general conditions. This general representation encompasses convex geometries, antimatroids, augmenting systems and distributive lattices. Two axiomatic characterizations are obtained. They both assume that the Shapley value is already defined on the combinatorial structures. The first one is restricted to pairs of players and is based on a generalization of a recursivity axiom that uniquely specifies the interaction index from the Shapley value when all coalitions are permitted. This unique correspondence cannot be maintained when some coalitions are forbidden. From this, a weak recursivity axiom is defined. We show that this axiom together with linearity and dummy player are sufficient to specify the interaction index. The second axiomatic characterization is obtained from the linearity, dummy player and partnership axioms. An interpretation of the interaction index in the context of surplus sharing is also proposed. Finally, our interaction index is instantiated to the case of games under precedence constraints. 相似文献
12.
This paper presents an axiomatization of the Shapley value. The balanced cycle contributions property is the key axiom in
this paper. It requires that, for any order of all the players, the sum of the claims from each player against his predecessor
is balanced with the sum of the claims from each player against his successor. This property is satisfied not only by the
Shapley value but also by some other values for TU games. Hence, it is a less restrictive requirement than the balanced contributions
property introduced by Myerson (International Journal of Game Theory 9, 169–182, 1980). 相似文献
13.
We define and characterize the class of all weighted solidarity values. Our first characterization employs the classical axioms determining the solidarity value (except symmetry), that is, efficiency, additivity and the A-null player axiom, and two new axioms called proportionality and strong individual rationality. In our second axiomatization, the additivity and the A-null player axioms are replaced by a new axiom called average marginality. 相似文献
14.
The paper suggests a similarity function for applications of empirical similarity theory in which the notion of similarity is asymmetric. I propose defining similarity in terms of a quasimetric. I suggest a particular quasimetric and explore the properties of the empirical similarity model given this function. The proposed function belongs to the class of quasimetrics induced by skewed norms. Finally, I provide a skewness axiom that, when imposed in lieu of the symmetry axiom in the main result of Billot et al. (2008), characterizes an exponential similarity function based on a skewed norm. 相似文献
15.
《Mathematical Social Sciences》1986,11(3):283-294
Auctions, public tenders, and fair division games are considered as special classes of games with incomplete information. The specialty of these games is that choosing a strategy in such a game amounts to displaying (the not necessarily true) preferences. Our main axiom of displayed envy-freeness states that according to his displayed preferences no player should prefer another player's net trade to his own. This axiom and the well-known property of incentive compatibility imply the rules of auctions and public tenders which are originally discussed by Vickrey. We consider our axiomatic characterization as a strong support for the Vickrey-rules. There is no obvious reason why the actually applied rules (e.g. the rules of public tenders in the Federal Republic of Germany) do often violate these rules.For fair division problems the two axioms are shown to be mutually inconsistent. By weakening the requirement of incentive compatibility we, nevertheless, can determine rules for fair division problems which are a reasonable analogue of the Vickrey-rules. Finally, it is discussed how our ideas can be extended to other allocation problems. 相似文献
16.
Eric Bahel 《International Journal of Game Theory》2011,40(3):551-589
In this paper, we study the Ranking property for discrete cost sharing methods. In the two-agent model, we characterize the
set of methods satisfying this axiom: the symmetry of the flow representing the method is necessary and sufficient for Ranking.
In higher dimensions (n ≥ 3), we identify strong implications of the axiom; however, we prove that these conditions are not sufficient to characterize
Ranking. For the so-called elementary fixed flows, we derive a necessary and sufficient condition. 相似文献
17.
Andrzej S. Nowak 《International Journal of Game Theory》1997,26(1):137-141
We prove that the Banzhaf value is a unique symmetric solution having the dummy player property, the marginal contributions property introduced by Young (1985) and satisfying a very natural reduction axiom of Lehrer (1988). 相似文献
18.
Encarnación Algaba René van den Brink Chris Dietz 《Journal of Optimization Theory and Applications》2017,172(3):1008-1022
Games under precedence constraints model situations, where players in a cooperative transferable utility game belong to some hierarchical structure, which is represented by an acyclic digraph (partial order). In this paper, we introduce the class of precedence power solutions for games under precedence constraints. These solutions are obtained by allocating the dividends in the game proportional to some power measure for acyclic digraphs. We show that all these solutions satisfy the desirable axiom of irrelevant player independence, which establishes that the payoffs assigned to relevant players are not affected by the presence of irrelevant players. We axiomatize these precedence power solutions using irrelevant player independence and an axiom that uses a digraph power measure. We give special attention to the hierarchical solution, which applies the hierarchical measure. We argue how this solution is related to the known precedence Shapley value, which does not satisfy irrelevant player independence, and thus is not a precedence power solution. We also axiomatize the hierarchical measure as a digraph power measure. 相似文献
19.
Strict Nash networks and partner heterogeneity 总被引:2,自引:0,他引:2
Pascal Billand Christophe Bravard Sudipta Sarangi 《International Journal of Game Theory》2011,40(3):515-525
This paper extends the two-way flow model of network formation initiated by Bala and Goyal (Econometrica 68(5):1181–1230,
2000) by allowing for partner heterogeneity. In our model if a player i forms a link with player j, then she pays a cost of c
j
and gets benefits of V
j
. Our main result consists of the characterization of strict Nash networks. We find that the introduction of partner heterogeneity
plays a major role in dramatically increasing the set of strict Nash equilibria. This result differs substantially from what
Galeotti et al. (Games Econ Behav 54(2):353–372, 2006) find in the two-way flow connections model of network formation with
player heterogeneity. 相似文献
20.
We show that Martin’s axiom for countable partial orders implies the existence of a countable dense homogeneous Bernstein
subset of the reals. Using Martin’s axiom we derive a characterization of the countable dense homogeneous spaces among the
separable metric spaces of cardinality less thanc. Also, we show that Martin’s axiom implies the existence of a subset of the Cantor set which isλ-dense homogeneous for everyλ <c. 相似文献