Hedonic coalition formation games with variable populations: core characterizations and (im)possibilities

We consider hedonic coalition formation games with variable sets of agents and extend the properties competition sensitivity and resource sensitivity (introduced by Klaus, Games Econ Behav 72:172–186, 2011, for roommate markets) to hedonic coalition formation games. Then, we show that on the domain of solvable hedonic coalition formation games, the Core is characterized by coalitional unanimity and Maskin monotonicity (see also Takamiya, Maskin monotonic coalition formation rules respecting group rights. Niigata University, Mimeo, 2010, Theorem 1). Next, we characterize the Core for solvable hedonic coalition formation games by unanimity, Maskin monotonicity, and either competition sensitivity or resource sensitivity (Corollary 2). Finally, and in contrast to roommate markets, we show that on the domain of solvable hedonic coalition formation games, there exists a solution not equal to the Core that satisfies coalitional unanimity, consistency, competition sensitivity, and resource sensitivity (Example 2).     

Equivalence of axioms for bankruptcy problems

The bankruptcy problem is concerned with how to divide the net worth of the bankrupt firm among its creditors. In this paper, we investigate the logical relations between various axioms in the context of bankruptcy. Those axioms are: population-and-resource monotonicity, consistency, converse consistency, agreement, and separability. In most axiomatic models, they are not directly related. However, we show that they are equivalent on the class of bankruptcy problems under minor additional requirements. Received: April 1998/Revised version: January 1999     

Characterization of the core in full domain marriage problems

In this paper, we study the core of two-sided, one-to-one matching problems. First, in a model in which agents have strict preferences over their potential mates and are allowed to remain single, we characterize the core as the unique solution that satisfies individual rationality, Pareto optimality, gender fairness, consistency, and converse consistency. Next, in a model that relaxes the constraint that agents have strict preferences over their potential mates, we show that no solution exists that satisfies Pareto optimality, anonymity, and converse consistency. In this full domain, we characterize the core by individual rationality, weak Pareto optimality, monotonicity, gender fairness, consistency, and converse consistency.     

Consistency and monotonicity in assignment problems

This paper presents axiomatic characterizations of the core of assignment problems. In the main axiomatization theorem we use six axioms including the consistency (CONS) and the weak pairwise-monotonicity (W.P.MON) which are firstly proposed and defined for this setup in the present paper. Since an assignment problem may be converted into a model of a private ownership economy with indivisible goods and the core of the assignment problem coincides with the set of the competitive allocations of the economy, our characterization theorems also give axiomatic characterizations of the set of competitive allocations. Because the consistency is a desirable property of resource allocation mechanisms, our main result gives a new normative implication of competitive equilibria.     

Weak monotonicity inequality and partial regularity for harmonic maps

The notion of locally weak monotonicity inequality for weakly harmonic maps is introduced and various results on this class of maps are obtained. For example, the locally weak monotonicity inequality is nearly equivalent to theε-regularity. Project supported by the National Natural Science Foundation of China (Grant No. 19571028) and the Guangdong Provincial Natural Science Foundation of China.     

单峰偏好下马斯金单调性与联盟防策略的等价性

本文证明了在单峰偏好域上Maskin单调性与防策略条件是等价的,并进一步证明了Maskin单调性与联盟防策略是等价的.从而推广了Muller-Satterthwaite(1977)在无限制强序域上得到的结论.在此基础上,利用Mollin(1980)在单峰偏好域上提出的防策略社会选择函数特征化定理,证明了在单峰偏好域上能够突破Muller-Satterthwaite不可能性定理所预示的消极结论.     

Basic topological and geometric properties of Cesàro-Orlicz spaces

Necessary and sufficient conditions under which the Cesàro-Orlicz sequence spaceces _ϕ is nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro-Orlicz spacesces _ϕ have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements inces _ϕ can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spacesces _ϕ are given.     

An axiomatic characterization of the Hirsch-index

The Hirsch-index is a well-known index for measuring and comparing the output of scientific researchers. The main contribution of this article is an axiomatic characterization of the Hirsch-index in terms of three natural axioms. Furthermore, two other scientific impact indices (called the w-index and the maximum-index) are defined and characterized in terms of similar axioms.     

Disagreement point axioms and the egalitarian bargaining solution

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.     

The relation between non-bossiness and monotonicity

It is a well-known fact that in some economic environments, non-bossiness and monotonicity are interrelated. In this paper, we have presented a new domain-richness condition called weak monotonic closedness, on which non-bossiness in conjunction with individual monotonicity is equivalent to monotonicity. Moreover, by applying our main result to several types of economies, we have obtained characterizations in terms of non-bossiness.     

Convex decomposition of games and axiomatizations of the core and the D-core

This paper provides an axiomatic framework to compare the D-core (the set of undominated imputations) and the core of a cooperative game with transferable utility. Theorem 1 states that the D-core is the only solution satisfying projection consistency, reasonableness (from above), (*)-antimonotonicity, and modularity. Theorem 2 characterizes the core replacing (*)-antimonotonicity by antimonotonicity. Moreover, these axioms also characterize the core on the domain of convex games, totally balanced games, balanced games, and superadditive games.      

A mean value for games with communication structures

The mean value is a new extension of the Shapley value for games with communication structure representable by a simple graph; only pairwise meetings can occur, although some of them might not be permitted. The new value is characterized by a set of axioms of which the one with the most far-reaching effect is an associated consistency property already used in various contexts. The mean value of an n-player unanimity game is the arithmetic average of the mean values of (n–1)-player unanimity games with connected support, which means games in which the deleted players are not articulation point of the considered graph.I wish to thank the anonymous referees for their helpful remarks. The usual disclaimer applies.Received: April 2002/Accepted: February 2004     

Discounting axioms imply risk neutrality

Although most applications of discounting occur in risky settings, the best-known axiomatic justifications are deterministic. This paper provides an axiomatic rationale for discounting in a stochastic framework. Consider a representation of time and risk preferences with a binary relation on a real vector space of vector-valued discrete-time stochastic processes on a probability space. Four axioms imply that there are unique discount factors such that preferences among stochastic processes correspond to preferences among present value random vectors. The familiar axioms are weak ordering, continuity and nontriviality. The fourth axiom, decomposition, is non-standard and key. These axioms and the converse of decomposition are assumed in previous axiomatic justifications for discounting with nonlinear intraperiod utility functions in deterministic frameworks. Thus, the results here provide the weakest known sufficient conditions for discounting in deterministic or stochastic settings. In addition to the four axioms, if there exists a von Neumann-Morgenstern utility function corresponding to the binary relation, then that function is risk neutral (i.e., affine). In this sense, discounting axioms imply risk neutrality.     

Non-cooperative implementation of the nucleolus: The 3-player case

I present a non-cooperative bargaining game, in which responders may exit at any time and have endogenous outside options. When the order of proposers corresponds to the power that players have in the underlying coalitional function, the unique Markov perfect equilibrium outcome of the game is the prenucleolus. The result holds for 3-player superadditive games. An example shows that it cannot be extented to the same class of games forn players. The mechanism is inspired by the consistency property of the prenucleolus.I am grateful to Vijay Krishna, Andreu Mas-Colell, Eric Maskin, Amy Salsbury, and an anonymous referee for helpful comments and suggestions.     

The consistency principle and an axiomatization of the α-core

This paper examines the α-core of strategic games by means of the consistency principle. I provide a new definition of a reduced game for strategic games. And I define consistency (CONS) and two forms of converse consistency (COCONS and COCONS^*) under this definition of reduced games. Then I axiomatize the α-core for families of strategic games with bounded payoff functions by the axioms CONS, COCONS^*, weak Pareto optimality (WPO) and one person rationality (OPR). Furthermore, I show that these four axioms are logically independent. In proving this, I also axiomatize the α-individually rational solution by CONS, COCONS and OPR for the same families of games. Here the α-individually rational solution is a natural extension of the classical `maximin' solution. Received: June 1998/Final version: 6 July 2001     

A labor market with heterogeneous firms and workers

A labor market where firms and workers are heterogeneous and may form more than one partnership is considered. A natural concept of core for such markets, different from the concept used by Thompson (1977), is defined. We show that the core is non-empty and is, in general, strictly greater than Thompson's core. Unlike Thompson, we found several dissimilarities between our model and the well known one-to-one case studied in Shapley and Shubik (1972). Received April 2001/Revised July 2002  This work was partially supported by FIPE-S?o Paulo and CNPq-Brazil.?I am in debt to David Gale and an anonymous referee and associate editor of IJGT whose comments and suggestions contributed for the improvement of this paper.     

Testing monotonicity over graph products

We consider the problem of monotonicity testing over graph products. Monotonicity testing is one of the central problems studied in the field of property testing. We present a testing approach that enables us to use known monotonicity testers for given graphs G₁, G₂, to test monotonicity over their product G₁ × G₂. Such an approach of reducing monotonicity testing over a graph product to monotonicity testing over the original graphs, has been previously used in the special case of monotonicity testing over [n]^d for a limited type of testers; in this article, we show that this approach can be applied to allow modular design of testers in many interesting cases: this approach works whenever the functions are boolean, and also in certain cases for functions with a general range. We demonstrate the usefulness of our results by showing how a careful use of this approach improves the query complexity of known testers. Specifically, based on our results, we provide a new analysis for the known tester for [n]^d which significantly improves its query complexity analysis in the low‐dimensional case. For example, when d = O(1), we reduce the best known query complexity from O(log ²n/ε) to O(log n/ε). © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Strict core fuzzy logics and quasi-witnessed models

In this paper we prove strong completeness of axiomatic extensions of first-order strict core fuzzy logics with the so-called quasi-witnessed axioms with respect to quasi-witnessed models. As a consequence we obtain strong completeness of Product Predicate Logic with respect to quasi-witnessed models, already proven by M.C. Laskowski and S. Malekpour in [19]. Finally we study similar problems for expansions with ??, define ??-quasi-witnessed axioms and prove that any axiomatic extension of a first-order strict core fuzzy logic, expanded with ??, and ??-quasi-witnessed axioms are complete with respect to ??-quasi-witnessed models.     

An axiomatic characterization of the Owen–Shapley spatial power index

We present an axiomatic characterization of the Owen–Shapley spatial power index for the case where issues are elements of two-dimensional space. This characterization employs a version of the transfer condition, which enables us to unravel a spatial game into spatial games connected to unanimity games. The other axioms include two conditions concerned particularly with the spatial positions of the players, besides spatial versions of anonymity and dummy. The last condition says that dummy players can be left out in a specific way without changing the power of the other players. We show that this condition can be weakened to requiring dummies to have zero power if we add a condition of positional continuity. We also show that the axioms in our characterization(s) are logically independent.