Additivity in bankruptcy problems and in allocation problems

We study the property of additivity in bankruptcy problems and in allocation problems. In bankruptcy problems we use this property to characterize the Talmudic rule proposed by Rabbi Ibn Ezra. Moreover we generalize this rule to every bankruptcy problem. Again, using additivity we characterize the rights egalitarian solution in allocation problems.     

Allocating Tradable Permits on the Basis of Market Price to Achieve Cost Effectiveness

It is a well known result that distributional constraints can lead to an imperfectly competitive permit market where the emission target is no longer met at least cost. In this paper, we suggest an allocation rule for tradable permits which can handle this problem. If the permit allocation is dependent on the market price for permits, this allocation rule can achieve both cost effectiveness and meet specific requirements for cost distribution across agents.     

Optimal combinatorial mechanism design

We consider an optimal mechanism design problem with several heterogenous objects and interdependent values. We characterize ex post incentives using an appropriate monotonicity condition and reformulate the problem in such a way that the choice of an allocation rule can be separated from the choice of the payment rule. Central to the analysis is the formulation of a regularity condition, which gives a recipe for the optimal mechanism. If the problem is regular, then an optimal mechanism can be obtained by solving a combinatorial allocation problem in which objects are allocated in a way to maximize the sum of virtual valuations. We identify conditions that imply regularity using the techniques of supermodular optimization.     

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.     

Allocation rules for land division

This paper studies the classical land division problem formalized by Steinhaus (Econometrica 16 (1948) 101-104) in a multi-profile context. We propose a notion of an allocation rule for this setting.  We discuss several examples of rules and properties they may satisfy. Central among these properties is division independence: a parcel may be partitioned into smaller parcels, these smaller parcels allocated according to the rule, leaving a recommended allocation for the original parcel. In conjunction with two other normative properties, division independence is shown to imply the principle of utilitarianism.     

STRATEGY‐PROOF ALLOCATION OF INDIVISIBLE GOODS AMONG COUPLES

We consider the problem of allocating indivisible goods among couples. Agents in a couple share the indivisible good assigned to them. The main result is that an allocation rule is strategy‐proof, neutral and non‐bossy if and only if it is serially dictatorial. An allocation rule is serially dictatorial if there is a priority order of couples and a function that identifies who chooses in each couple, such that for all preference profiles, a good assigned to couple i is the best element according to the preference of the identified agent in couple i among the remaining goods when the couples with higher priorities have made their choice.     

Weak monotonicity and Bayes–Nash incentive compatibility

An allocation rule is called Bayes–Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents' types form a Bayes–Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes–Nash incentive compatible allocation rules in social choice settings where agents have multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived by constructing complete directed graphs on agents' type spaces with cost of manipulation as lengths of edges. Weak monotonicity of the allocation rule corresponds to the condition that all 2-cycles in these graphs have non-negative length. For the case that type spaces are convex and the valuation for each outcome is a linear function in the agent's type, we show that weak monotonicity of the allocation rule together with an integrability condition is a necessary and sufficient condition for Bayes–Nash incentive compatibility.     

Weak monotonicity and Bayes–Nash incentive compatibility

An allocation rule is called Bayes–Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents' types form a Bayes–Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes–Nash incentive compatible allocation rules in social choice settings where agents have multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived by constructing complete directed graphs on agents' type spaces with cost of manipulation as lengths of edges. Weak monotonicity of the allocation rule corresponds to the condition that all 2-cycles in these graphs have non-negative length. For the case that type spaces are convex and the valuation for each outcome is a linear function in the agent's type, we show that weak monotonicity of the allocation rule together with an integrability condition is a necessary and sufficient condition for Bayes–Nash incentive compatibility.     

Core is manipulable via segmentation

Any allocation rule that picks only core allocations is manipulable via segmentation. That is, there exists an economy with a coalition of agents such that, once this coalition splits momentarily from the rest of the economy and institutes the allocation rule within itself, no matter which individually rational sub-allocation the complementary coalition picks, when we paste all the agents back together at their new endowments and apply the allocation rule to this “collage” economy, each member of the former coalition will be strictly better off than under direct application of the allocation rule to the original economy.     

GAINS FROM TRADE

In a social choice context, we ask whether there exists a rule in which nobody loses under trade liberalization. We consider a resource allocation problem in which the traded commodities vary. We propose an axiom stating that enlarging the set of tradable commodities hurts nobody. We show that if a rule satisfies this axiom, together with an allocative efficiency axiom and an institutional constraint axiom stating that only preferences over tradable commodities matter, gains from trade can be given to only one individual in the first step of liberalization.     

Coalitional strategy-proofness and fairness

This paper considers the problem of assigning a finite number of indivisible objects, like jobs, houses, positions, etc., to the same number of individuals. There is also a divisible good (money) and the individuals consume money and one object each. The class of fair allocation rules that are strategy-proof in the strong sense that no coalition of individuals can improve the allocation for all of its members, by misrepresenting their preferences, is characterized. It turns out that given a regularity condition, the outcome of a fair and coalitionally strategy-proof allocation rule must maximize the use of money subject to upper quantity bounds determined by the allocation rule. If available money is nonnegative, objects may be jobs and the distribution of money a wage structure. If available money is negative, the formal model may reflect a multi-object auction. In both cases fairness means equilibrium, i.e., that each individual receives a most demanded object. I would like to thank Tommy Andersson, Bo Larsson, Zaifu Yang and the participants of the seminars in Copenhagen and Lund for helpful comments on this paper. I will also thank an anonymous referee for very valuable comments. Financial support from The Jan Wallander and Tom Hedelius Foundation is gratefully acknowledged.     

Cost monotonicity, consistency and minimum cost spanning tree games

We propose a new cost allocation rule for minimum cost spanning tree games. The new rule is a core selection and also satisfies cost monotonicity. We also give characterisation theorems for the new rule as well as the much-studied Bird allocation. We show that the principal difference between these two rules is in terms of their consistency properties.     

Maximal Domain of Preferences in the Division Problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, then the uniform allocation rule is the unique strategy-proof, efficient, and anonymous rule. We identify the maximal set of preferences, containing the set of single-peaked preferences, under which there exists at least one rule satisfying the properties of strategy-proofness, efficiency, and strong symmetry. In addition, we show that our characterization implies a slightly weaker version of Ching and Serizawa's (1998) result. Journal of Economic Literature Classification Numbers: D71, D78, D63.     

新制度经济学的产权界定理论述评

发现产权界定在资源配置和市场交易中的重要作用是科斯对新制度经济学发展的一个巨大贡献。在科斯之后,德姆塞茨揭示了产权界定的形式及其发生的机理,波斯纳给出了产权界定应遵循的一般性准则,巴泽尔揭示了产权界定的相对性和公共领域,诺思则对国家界定产权的目的、优势和存在的问题等作了进一步的研究。     

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.     

Economic (dis)integration in the presence of evolutionary learning

We use a two-factor, two-sector model to study the effects of economic integration and its reversal in the presence of input-generated external economies in one of the sectors. The equilibrium selection problem that arises is solved by applying a simple trial-and-error learning rule. Economic integration can take individual economies ridden with coordination failures to better equilibria, i.e., can solve the coordination problem. We show that integration (and disintegration) may generate cycles in wages, rentals and the sectoral allocation of factors.JEL Classification: F15, F16, F37 Corespondence to: Diego Méndez-Carbajo     

SHARECROPPING,LAND EXPLOITATION AND LAND‐IMPROVING INVESTMENTS*

This paper analyses the tenancy problem in a dynamic setup and addresses two long‐standing issues: inefficiency and lack of investment. It considers the problems that the tenant, with a shorter‐term interest in the farm than the landlord, might overexploit the land to maximize immediate returns even at the cost of future damages, and under‐supply long‐run productivity improving investments in land. I show that the efficient (first‐best) levels of input use and investment can be achieved (both in the steady state and in transition) by a suitable share contract which, by dampening incentives to maximize current returns, addresses the land exploitation problem, and by an appropriate cost allocation rule which can address the investment problem.     

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.     

The Dynamic Vickrey Auction

We study the efficient allocation of a single object over a finite time horizon. Buyers arrive randomly over time, are long-lived, and have independent private values. The valuation of a buyer may depend on the time of the allocation in an arbitrary way. We construct an incentive compatible mechanism in which (A) there is a single financial transaction (with the buyer), (B) ex-post participation constraints are fulfilled, (C) there is no positive transfer to any agent and (D) payments are determined online. We exploit that under the efficient allocation rule, there is a unique potential winning period for each buyer. This reduces the multidimensional type to one dimension and the payment of the winner can be defined as the lowest valuation for the potential winning period, with which the buyer would have won the object. In a static model, this payment rule coincides with the payment rule of the Vickrey Auction.     

A Risk‐Dominant Allocation: Maximizing Coalition Stability

This paper presents a rule to allocate a coalition’s worth for superadditive games with positive externalities. The allocation rule awards each member their outside payoff, plus an equal share of the surplus. The resulting allocation maximizes coalition stability. Stable coalitions are Strong Nash equilibria since no subset of members has an incentive to leave. Similarly, no subset of non‐members has an incentive to join a stable coalition if the game is concave in this region. The allocation is risk‐dominant. All stable coalitions are robust to the maximum probability of 50% that players’ deviate from their individual best‐responses. The paper compares the allocation to the Shapley value and the Nash bargaining solution, and illustrates why these traditional rules result in small coalitions when applied to issues such as international environmental agreements.