Non-manipulable division rules in claim problems and generalizations

When resources are divided among agents, the characteristics of the agents are taken into consideration. A simple example is the bankruptcy problem, where the liquidation value of a bankrupt firm is divided among the creditors based on their claims. We characterize division rules under which no group of agents can increase the total amount they receive by transferring their characteristics within the group. By allowing agents’ characteristics to be multi-dimensional and choosing the meaning of variables appropriately, our model can subsume a number of existing and new allocation problems, such as cost sharing, social choice with transferable utilities, income redistribution, bankruptcy with multiple types of assets, probability updating, and probability aggregation. A number of existing and new results in specific problems are obtained as corollaries.     

No profitable decompositions in quasi-linear allocation problems

We study the problem of allocating a bundle of perfectly divisible private goods from an axiomatic point of view, in situations where compensations can be made through monetary transfers. The key property we impose on the allocation rule requires that no agent should be able to gain by decomposing the problem into sequences of subproblems. Combined with additional standard properties, it leads to a characterization of the rule that shares the total surplus equally. Hence a traditional welfarist rule emerges as the unique consequence of our axioms phrased in a natural economic environment.     

Optimal personal bankruptcy design under moral hazard

In this paper, we develop a normative theory of unsecured consumer credit and personal bankruptcy based on the optimal trade-off between incentives and insurance. First, in order to characterize this trade-off, we solve a dynamic moral hazard problem in which agents' private effort decisions influence the life-cycle profiles of their earnings. We then show how the optimal allocation of individual effort and consumption can be implemented in a market equilibrium in which (i) agents and intermediaries repeatedly trade secured and unsecured debt instruments, and (ii) agents obtain (restricted) discharge of their unsecured debts in bankruptcy. The structure of this equilibrium and the associated restrictions on debt discharge closely match the main qualitative features of personal credit markets and bankruptcy law that actually exist in the United States.     

Sharing-group allocation problems

We deal with allocation problems among sharing groups. We introduce some allocation rules and axioms. The egalitarian rule is characterized by equal treatment of equal groups, solidarity, and group consistency.     

An axiomatic characterization of the Baker-Thompson rule

The airport problem is a widely studied allocation problem, with the aim of providing simple and fair sharing rule for the landing fees. In this note we introduce some fairness criteria and characterize the classical Baker-Thompson allocation rule.     

Allocation problems among sharing groups

We deal with allocation problems among sharing groups. There are n agents. The agents are divided into several sharing groups. A homogeneous good is allocated among sharing groups rather than among the agents. The good is a private good for sharing groups, and a public good for the members of each sharing group. That is, all of them in the same sharing group can consume it without rivalry. We introduce some allocation rules and axioms. The utilitarian allocation rule and the egalitarian allocation rule are characterized by some axioms.     

论我国破产重整程序存在的问题——以英国法为视角

我国2006年颁布的《企业破产法》首次引入了重整制度,试图给陷入财务困境又有重生希望的企业提供一个法律保障机制。但实践中重整程序应用的不多且条文本身也存在着各种问题。在制度设计上,如程序的启动、自动冻结的效果、破产管理人权利的分配、法院的介入以及强制裁定权的运用等方面存在着缺陷。英国公司重整制度自上世纪八十年代以来进行了多次重大修改,其制度的改革和完善给我国立法者提供了很多启示。     

Game theoretic analysis of a bankruptcy problem from the Talmud

For three different bankruptcy problems, the 2000-year old Babylonian Talmud prescribes solutions that equal precisely the nucleoli of the corresponding coalitional games. A rationale for these solutions that is independent of game theory is given in terms of the Talmudic principle of equal division of the contested amount; this rationale leads to a unique solution for all bankruptcy problems, which always coincides with the nucleolus. Two other rationales for the same rule are suggested, in terms of other Talmudic principles. (Needless to say, the rule in question is not proportional division).     

Prices in Mixed Cost Allocation Problems

We consider mixed cost allocation problems, i.e., joint cost problems that involve two types of heterogeneous outputs, divisible and indivisible. The Aumann–Shapley price mechanism is extended to this setting. We also present a set of properties which characterize this cost sharing rule. Journal of Economic Literature Classification numbers: D63, C79.     

A characterization of the Shapley value in queueing problems

A set of agents stand to receive a service. No two agents can be served simultaneously. A queue has to be organized, and agents having to wait should receive monetary compensations. We characterize the rule assigning positions in the queue and compensations corresponding to the payoffs recommended by the Shapley value of the associated cooperative game. We use a property of independence with respect to increase in some agents’ impatience, and an equal responsibility property.     

Minimum cost spanning tree problems with groups

We study minimum cost spanning tree problems with groups. We assume that agents are located in different villages, cities, etc. The groups are the agents of the same village. We introduce a rule for dividing the cost of connecting all agents to the source among the agents taking into account the group structure. We characterize this rule with several desirable properties. We prove that this rule coincides with the Owen value of the TU game associated with the irreducible matrix.     

Extending the Nash solution to choice problems with reference points

In 1985 Aumann axiomatized the Shapley NTU value by non-emptiness, efficiency, unanimity, scale covariance, conditional additivity, and independence of irrelevant alternatives. We show that, when replacing unanimity by “unanimity for the grand coalition” and translation covariance, these axioms characterize the Nash solution on the class of n-person choice problems with reference points. A classical bargaining problem consists of a convex feasible set that contains the disagreement point here called reference point. The feasible set of a choice problem does not necessarily contain the reference point and may not be convex. However, we assume that it satisfies some standard properties. Our result is robust so that the characterization is still valid for many subclasses of choice problems, among those is the class of classical bargaining problems. Moreover, we show that each of the employed axioms – including independence of irrelevant alternatives – may be logically independent of the remaining axioms.     

Ambiguity aversion and trade

What is the effect of ambiguity aversion on trade? Although in a Bewley??s model, ambiguity aversion always leads to less trade; in other models, this is not always true. However, we show that if the endowments are unambiguous, then more ambiguity aversion implies less trade for a very general class of preferences. The reduction in trade caused by ambiguity aversion can be as severe as to lead to no trade. In an economy with MEU decision makers, we show that if the aggregate endowment is unanimously unambiguous, then every Pareto optima allocation is also unambiguous. We also characterize the situation in which every unanimously unambiguous allocation is Pareto optimal. Finally, we show how our results can be used to explain the home-bias effect. As a useful result for our methods, we also obtain an additivity theorem for CEU and MEU decision makers that does not require comonotonicity.     

Bidding for surplus in network allocation problems

In this paper we study non-cooperative foundations of network allocation rules. We focus on three allocation rules: the Myerson value, the position value and the component-wise egalitarian solution. For any of these three rules we provide a characterization based on component efficiency and some balanced contribution property. Additionally, we present three mechanisms whose equilibrium payoffs are well defined and coincide with the three rules under consideration if the underlying value function is monotonic. Non-monotonic value functions are shown to deal with allocation rules applied to monotonic covers. The mechanisms are inspired by the implementation of the Shapley value by Pérez-Castrillo and Wettstein [Bidding for the surplus: a non-cooperative approach to the Shapley value, J. Econ. Theory 100 (2) (2001) 274-294].     

Kantian equilibria of a class of Nash bargaining games

We study Kantian equilibria of an $n$-player bargaining game, which is a modified version of the well-known divide-the-dollar game. We first show that the Kantian equilibrium exists under fairly minimal assumptions. Second, if the bankruptcy rule used satisfies equal treatment of equals, and is almost nowhere proportional, then only equal division can prevail in any Kantian equilibrium. On the other hand, we show that an “anything goes” type result emerges only under the proportional rule. Finally, using hybrid bankruptcy rules that we construct in a novel fashion, we can characterize the whole equilibrium set. Our results highlight the interactions between institutions (axiomatic properties of division rules) and agents' equilibrium behavior.     

Comparable Axiomatizations of Two Allocation Rules for Cooperative Games with Transferable Utility and Their Subclass of Data Games

The axiom of balanced collective contributions is introduced as a collective variant of the axiom of balanced contributions proposed by Myerson. It requires the identical average impact of the withdrawal of any agent from a game on the remaining population. It turns out that the axiom of balanced collective contributions and the classical axiom of efficiency characterize the equal allocation of nonseparable costs, an allocation rule that is extensively used in cost allocation problems and in accounting. In particular, the equal allocation of nonseparable costs coincides with the nucleolus on the class of data games within the European REACH legislation. While our result does not hold on data games, extra axioms enable provision of comparable characterizations of the equal allocation of nonseparable costs and the Shapley value on this class of games.     

Credit risk in general equilibrium

This paper contributes to the literature on default in general equilibrium. Borrowing and lending takes place via a clearing house (bank) that monitors agents and enforces contracts. Our model develops a concept of bankruptcy equilibrium that is a direct generalization of the standard general equilibrium model with financial markets. Borrowers may default in equilibrium and returns on loans are determined endogenously. Restricted to a special form of mean variance preferences, we derive a version of the capital asset pricing model with bankruptcy. In this case, we can characterize equilibrium prices and allocations and discuss implications for credit risk modeling.     

General allocation problems with single-peaked preferences: path-independence and related topics

We face the problem of allocationg a fixed amount of a perfectly divisible good among a group of agents with single-peaked preferences. We survey the three different cases studied in the literature: the pure distribution case, the redistribution case, and the gerneral case. The so called general case provide with a natural framework to analyze the idea of path-independence. In this framework, we explore the existence of rules fulfilling this property. Our first result is negative: a strong version of this property cannot be fulfilled together with efficiency. Nonetheless, some restricted versions of the path-independence property are compatible with interesting properties, in particular no manipulability, and no envy. We then identify two solutions satisfying this sort of property: the equal distance rule, and a new extension of the uniform rule.     

Valuation in infinite-horizon sequential markets with portfolio constraints

Summary. We develop a theory of valuation of assets in sequential markets over an infinite horizon and discuss implications of this theory for equilibrium under various portfolio constraints. We characterize a class of constraints under which sublinear valuation and a modified present value rule hold on the set of non-negative payoff streams in the absence of feasible arbitrage. We provide an example in which valuation is non-linear and the standard present value rule fails in incomplete markets. We show that linearity and countable additivity of valuation hold when markets are complete. We present a transversality constraint under which valuation is linear and countably additive on the set of all payoff streams regardless of whether markets are complete or incomplete. Received: March 9, 2000; revised version: February 13, 2001     

No-envy in queueing problems

We explore the implications of no-envy(Foley 1967) in the context of queueing problems. We identify an easy way of checking whether a rule satisfies efficiencyand no-envy. The existence of such a rule can easily be established. Next, we ask whether there is a rule satisfying efficiency and no-envytogether with an additional solidarity requirement how agents should be affected as a consequence of changes in the waiting costs. However, there is no rule satisfying efficiency, noenvy, and either one of two cost monotonicity axioms. To remedy the situation, we propose modifications of no-envy, adjusted no-envyand backward/forward no-envy. Finally, we discuss whether three fairness requirements, no-envy, the identical preferences lower bound, and egalitarian equivalence, are compatible in this context.