Egalitarian division under Leontief Preferences

We consider the problem of fairly dividing $l$ divisible goods among $n$ agents with the generalized Leontief preferences. We propose and characterize the class of generalized egalitarian rules which satisfy efficiency, group strategy-proofness, anonymity, resource monotonicity, population monotonicity, envy-freeness and consistency. On the Leontief domain, our rules generalize the egalitarian-equivalent rules with reference bundles. We also extend our rules to agent-specific and endowment-specific egalitarian rules. The former is a larger class of rules satisfying all the previous properties except anonymity and envy-freeness. The latter is a class of efficient, group strategy-proof, anonymous and individually rational rules when the resources are assumed to be privately owned.     

Payoff equivalence between Bayesian and ex post individually rational dominant strategy mechanisms

Summary. An efficient, interim individually rational, ex post budget balanced Bayesian mechanism is shown to be payoff equivalent to an ex post individually rational and ex ante budget balanced dominant strategy mechanism. This result simplifies the search for mechanisms that implement efficient allocation rules by pointing to a class of Groves mechanisms. It eliminates the strict requirement of common knowledge of priors and can be applied to many problems of incomplete information. Received: October 22 1996; revised version: November 25, 1997     

Local envy-freeness and equal-income Walrasian allocations

This paper introduces a local version of envy-freeness and investigates its implications in a continuum agent economy with connected preferences. We show that the set of locally envy-free and Pareto efficient allocations coincides with the set of equal-income Walrasian allocations.     

Market structure and matching with contracts

Ostrovsky (2008) [9] develops a theory of stability for a model of matching in exogenously given networks. For this model a generalization of pairwise stability, chain stability, can always be satisfied as long as agents' preferences satisfy same side substitutability and cross side complementarity. Given this preference domain I analyze the interplay between properties of the network structure and (cooperative) solution concepts. The main structural condition is an acyclicity notion that rules out the implementation of trading cycles. It is shown that this condition and the restriction that no pair of agents can sign more than one contract with each other are jointly necessary and sufficient for (i) the equivalence of group and chain stability, (ii) the core stability of chain stable networks, (iii) the efficiency of chain stable networks, (iv) the existence of a group stable network, and (v) the existence of an efficient and individually stable network. These equivalences also provide a rationale for chain stability in the unrestricted model. The (more restrictive) conditions under which chain stability coincides with the core are also characterized.     

A general characterization of interim efficient mechanisms for independent linear environments

We consider the class of Bayesian environments with independent types, and utility functions which are both quasi-linear in a private good and linear in a one-dimensional private-value type parameter. We call these independent linear environments. For these environments, we fully characterize interim efficient allocation rules which satisfy interim incentive compatibility and interim individual rationality constraints. We also prove that they correspond to decision rules based on virtual surplus maximization, together with the appropriate incentive taxes. We illustrate these techniques with applications to auction design and public good provision.     

Weak stability and a bargaining set for the marriage model

In this note we introduce weak stability, a relaxation of the concept of stability for the marriage model by assuming that the agents are no longer myopic in choosing a blocking pair. The new concept is based on threats within blocking pairs: an individually rational matching is weakly stable if for every blocking pair one of the members can find a more attractive partner with whom he forms another blocking pair for the original matching. Our main result is that under the assumption of strict preferences, the set of weakly stable and weakly efficient matchings coincides with the bargaining set of Zhou (1994, Games Econ. Behav. 6, 512–526) for this context.     

Convergence under replication of rules to adjudicate conflicting claims

We study the behavior of rules for the adjudication of conflicting claims when there is a large number of claimants with small claims. We model such situations by replicating some basic problem. We show that under replication, the random arrival rule [Math. Soc. Sci. 2 (1982) 345] behaves like the proportional rule, the rule that is the most often recommended in this context. Also, under replication, the minimal overlap rule [Math. Soc. Sci. 2 (1982) 345] behaves like the constrained equal losses rule, the rule that selects a division at which all claimants experience equal losses subject to no-one receiving a negative amount.     

Choosing and sharing

Implementing a project, like a nationwide nuclear waste disposal, which benefits all involved agents but brings major costs only to the host is often problematic. In practice, revelation issues and redistributional concerns are significant obstacles to achieving stable agreements. We address these issues by proposing the first mechanism to select the efficient site (the host with the lowest cost) while simultaneously allowing for the implementation of any individually rational division of the whole hosting cost. The subgame perfect Nash equilibria of our simple mechanism are efficient, budget-balanced and individually rational. Moreover, the truthful equilibrium is immune to coalitional deviations.     

Designing international environmental agreements under participation uncertainty

Traditional international environmental agreement (IEA) models usually use some specific contribution rules, which either fail to provide sufficient incentives for cooperation, or ignore the loss from participation uncertainty. Can more general rules overcome these problems and improve the performance of IEAs? This paper analyzes the endogenous determination of contribution rules from a class of general rules through a three-stage coalition formation game under participation uncertainty. In stage one, a designer chooses a contribution rule, which, depending on the size of the signatories’ coalition formed in stage two, specifies the action each signatory should take in stage three. A contribution rule is said to be optimal when it maximizes the expected payoff of signatories. We provide an algorithm to determine an optimal rule. When uncertainty is either sufficiently large or equal to zero, the optimal rule coincides with some existing rules in the literature. However, when the uncertainty is neither large nor small, the optimal rule outperforms other rules in terms of signatories’ payoff.     

A Unique Informationally Efficient Allocation Mechanism In Economies With Consumption Externalities*

This article investigates the informational requirements of resource allocation processes in pure exchange economies with consumption externalities. It is shown that the distributive Lindahl mechanism has a minimal informational size of the message space, and thus it is informationally the most efficient allocation process that is informationally decentralized and realizes Pareto‐efficient allocations over the class of economies that include nonmalevolent economies. Furthermore, it is shown that the distributive Lindahl mechanism is the unique informationally efficient decentralized mechanism that realizes Pareto‐efficient and individually rational allocations over a certain class of nonmalevolent economies.     

Naive Adaptive Behavior and the Observability of Gambles

This paper considers a class of naive adaptive learning rules in a social setting. They generalize biological selection and have become relevant in economic theory as a consequence of their use in evolutionary game models. The environment considered here is nonstrategic but includes gambles which are more or less completely observed in each period. In the long run, individuals are more averse to a gamble which is less observable, other things being equal, and may violate first-order stochastic dominance. Thus these rules need not be consistent with rational behavior in the usual sense.Journal of Economic LiteratureClassification Numbers: D83, C72.     

Efficiency, monotonicity and rationality in public goods economies

Summary. In economies with public goods, we identify a necessary and sufficient condition for the existence of cost monotonic, Pareto optimal and individually rational mechanisms. These exist if and only if the preferences of the agents satisfy what we call the equal ordering property. We also show that when this condition holds the egalitarian equivalent correspondence is the only cost monotonic selection from the core of the economy. Furthermore, it is unambiguous in the sense that the agents are indifferent among all the allocations in it. Received: February 26, 1996; revised version: January 31, 1997     

Strategy-proof contract auctions and the role of ties

A contract auction establishes a contract between a center and one of the bidders. As contracts may describe many terms, preferences over contracts typically display indifferences. The Qualitative Vickrey Auction (QVA) selects the best contract for the winner that is at least as good for the center as any of the contracts offered by the non-winning players. When each bidder can always offer a contract with higher utility for the center at an arbitrarily small loss of her own utility, the QVA is the only mechanism that is individually rational, strategy-proof, selects stable outcomes, and is Pareto efficient. For general continuous utility functions, a variant of the QVA involving fixed tie-breaking is strategy-proof and also selects stable outcomes. However, there is no mechanism in this setting that in addition also selects Pareto efficient outcomes.     

Agreeing on Efficient Emissions Reduction

We propose a simple contest‐based mechanism providing incentives to reduce harmful emissions to their efficient level without infringing upon productive efficiency. Participation in the most stylized form of the scheme is voluntary and individually rational; all rules are mutually agreeable and are unanimously adopted if proposed. The scheme balances its budget and requires no principal. In a perhaps more realistic stochastic output version, which could potentially inform policy decisions, we show that the transfers required by the efficient mechanism create a mutual insurance motive that can serve as an effective rationale for the (gradual) formation of international environmental agreements.     

A characterization of a family of rules for the adjudication of conflicting claims

We consider the problem of adjudicating conflicting claims, and characterize the family of rules satisfying four standard invariance requirements, homogeneity, two composition properties, and consistency. It takes as point of departure the characterization of the family of two-claimant rules satisfying the first three requirements, and describes the restrictions imposed by consistency on this family and the further implications of this requirement for problems with three or more claimants. The proof, which is an alternative to Moulinʼs original proof [Moulin, H., 2000. Priority rules and other asymmetric rationing methods. Econometrica 68, 643–684], is based on a general method of constructing consistent extensions of two-claimant rules [Thomson, W., 2007. On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach. Rev. Econ. Design 11, 225–251], which exploits geometric properties of paths of awards, seen in their entirety.     

Profit sharing in unique Nash equilibrium: Characterization in the two-agent case

Two agents jointly operate a decreasing marginal returns technology to produce a private good. We characterize the class of output-sharing rules for which the labor-supply game has a unique Nash equilibrium. It consists of two families: rules of the serial type which protect a small user from the negative externality imposed by a large user, and rules of the reverse serial type, where one agent effectively employs the other agent's labor. Exactly two rules satisfy symmetry; a result in sharp contrast with Moulin and Shenker's characterization of their serial mechanism as the unique cost-sharing rule satisfying the same incentives property [Moulin, H., Shenker, S., 1992. Serial cost sharing. Econometrica 60 (5), 1009–1037]. We also show that the familiar stand-alone test characterizes the class of fixed-path methods under our incentives criterion [Friedman, E.J., 2004. Strong monotonicity in surplus sharing. Econ. Theory 23, 643–658].     

Fiscal Constitutions

In this paper we examine how taxes, subsidies and the design of constitutional agendas should be regulated in order to allow for an efficient allocation of public goods and a limitation of tax distortions. We show that if public goods are socially desirable, the simple majority rule, combined with taxation constrained to majority winners or a ban on subsidies, can achieve several desirable objectives. Equal treatment regarding taxes and subsidies is undesirable. Super majority rules and equal treatment of all citizens with respect to taxes and subsidies, however, are first-best provided public goods are socially undesirable. Finally, we suggest that constitutions with amendments eliminate excessive taxation and allow treatment rules to universally improve welfare.     

Bundling as an optimal selling mechanism for a multiple-good monopolist

Multiple objects may be sold by posting a schedule consisting of one price for each possible bundle and permitting the buyer to select the price-bundle pair of his choice. We identify conditions that must be satisfied by any price schedule that maximizes revenue within the class of all such schedules. We then provide conditions under which a price schedule maximizes expected revenue within the class of all incentive compatible and individually rational mechanisms in the n-object case. We use these results to characterize environments, mainly distributions of valuations, where bundling is the optimal mechanism in the two and three good cases.     

Lorenz rankings of rules for the adjudication of conflicting claims

For the adjudication of conflicting claims, we develop three general approaches to obtain Lorenz rankings of rules. Our first approach concerns a parameterized family that contains several important rules (Thomson in Soc Choice Welf 31:667?C692, 2008). We give a condition that the parameters defining two members of the family should satisfy for one of them to Lorenz dominate the other. Our second approach exploits the concept of ??consistency?? (Young in Math Oper Res 12:398?C414, 1987). We derive a criterion to deduce Lorenz domination for arbitrarily many claimants from Lorenz domination in the two-claimant case. Our third approach is based on the notion of an ??operator?? on the space of rules (Thomson and Yeh in J Econ Theory 143:177?C198, 2008). We develop conditions under which operators preserve the Lorenz order, or reverse it. As corollaries of our general theorems, we obtain rankings of most of the rules that have been discussed in the literature.     

Adverse selection under ignorance

Summary. We examine an adverse selection relationship in which the principal may ignore the ex ante distribution of the agent's types. The principal's behavior is described by a disutility function that covers the standard minimax regret and minimax loss criteria. We show that the incentive compatible and individually rational mechanism, which minimizes the maximal (or the minimal) principal's disutility over a set of priors, requires the efficient agents to realize the corresponding first-best actions and may demand actions lower than the first-best ones from less efficient agents. We also analyze the qualitative differences between the case in which the principal considers regrets and the case in which he considers losses. Received: 19 October 1998; revised version: 9 November 1999