Bancruptcy in a model of unsecured claims

Summary. We study a two periods model of incomplete markets with nominal assets unsecured by collateral, where agents can go bankrupt but there are no bankruptcy penalties entering directly in the utility function. We address two cases: first, a proportional reimbursement rule under bounded short sales and limited liability and, secondly, a nonproportional reimbursement rule, favoring smaller claims, without bounds on short-sales, but assuming that liability approaches total garnishment as debt goes to infinity. Received: September 10, 1998; revised version: August 6, 2001     

Asymmetric rules for claims problems without homogeneity

We introduce a general class of rules for claims problems, called the difference rules, and demonstrate that a rule satisfies composition down and composition up if and only if it is a difference rule. We show that these rules are very simple to describe when there are two agents. In a variable population framework, we introduce a family of rules satisfying consistency, composition down, and composition up, which we term the logarithmic-proportional rules. These rules satisfy neither symmetry nor homogeneity.     

Operators for the adjudication of conflicting claims

We consider the problem of allocating some amount of an infinitely divisible and homogeneous resource among agents having claims on this resource that cannot be jointly honored. A “rule” associates with each such problem a feasible division. Our goal is to uncover the structure of the space of rules. For that purpose, we study “operators” on the space, that is, mappings that associate to each rule another one. Duality, claims truncation, and attribution of minimal rights are the operators we consider. We first establish a number of results linking them. Then, we determine which properties of rules are preserved under each of these operators, and which are not.     

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.     

Equilibrium with limited-recourse collateralized loans

We address a general equilibrium model with limited-recourse collateralized loans and securitization of debts. Each borrower is required to pledge physical collateral, and bankruptcy is filed against him if claims are not fully honored. Moreover, agents have a positive amount of wealth exempt from garnishment and, for at least a fraction of them, commodities used as collateral are desirable. In this context, equilibrium exists for any continuous garnishment rule and multiple types of reimbursement mechanisms.     

Rules of evidence and liability in contract litigation: The efficiency of the General Dynamics rule

We examine rules of evidence and liability in contract litigation. When a contractor fails to perform, it has a legal defense that the buyer withheld private information relevant to the performance of the contract. Suppose the buyer claims that admitting evidence for the defense would compromise a valuable secret, for example, a state secret, what should the legal rule be? We show that the evidentiary rules introduced by the Supreme Court in General Dynamics v. U.S. lead to a more efficient outcome than either a strict liability rule or an evidentiary rule requiring the disclosure of the buyer's private information.     

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.     

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.     

Cost sharing with multiple technologies

We study cost sharing problems where gains from cooperation can come from the presence of other agents, such as when agents share their technologies. A simple model is built, where economies of scale are eliminated in order to study this effect. We use as the key axiom the property that, if an agent does not improve the technology of any coalition he joins, he should not get any part of the gain from cooperation. With properties of linearity and symmetry, this axiom characterizes a well-defined set of rules. From this set, we propose a rule derived from the familiar Shapley value. We show that it is the only rule in that set satisfying an upper-limit property on individual cost allocations or a monotonicity property when technology improves. We also derive a distinct rule using a property that ensures that no coalition has an incentive to manipulate the individual demands of its members.     

Cost sharing with multiple technologies

We study cost sharing problems where gains from cooperation can come from the presence of other agents, such as when agents share their technologies. A simple model is built, where economies of scale are eliminated in order to study this effect. We use as the key axiom the property that, if an agent does not improve the technology of any coalition he joins, he should not get any part of the gain from cooperation. With properties of linearity and symmetry, this axiom characterizes a well-defined set of rules. From this set, we propose a rule derived from the familiar Shapley value. We show that it is the only rule in that set satisfying an upper-limit property on individual cost allocations or a monotonicity property when technology improves. We also derive a distinct rule using a property that ensures that no coalition has an incentive to manipulate the individual demands of its members.     

Strategyproof and Nonbossy Multiple Assignments

We consider the allocation of heterogeneous indivisible objects without using monetary transfers. Each agent may be assigned more than one object. We show that an allocation rule is strategyproof, nonbossy, and satisfies citizen sovereignty if and only if it is a sequential dictatorship . In a sequential dictatorship agents are assigned their favorite objects that are still available, according to a sequentially endogenously determined hierarchy of the agents. We also establish that replacing nonbossiness by a stronger criterion restricts the characterized class of allocation rules to serial dictatorships , in which the hierarchy of the agents is fixed a priori.     

The nudge wars: A modern socialist calculation debate

We investigate the claims of behavioral paternalism in the more realistic framework of complex choice. In particular, we analyze the claims made by behavioral paternalists that predictive analytics over large amounts of data will make it possible to target and successfully implement purportedly welfare-enhancing nudges deemed to make nudged agents better off “as judged by themselves” (AJBT). We draw parallels between the socialist calculation debate and nudge theoretical arguments, particularly the libertarian socialism of H. D. Dickinson and the libertarian paternalism of Cass Sunstein and Richard Thaler. We find that if actual idealized behavior is a more complicated process of recursive feedback using a knowledge classification method, behavioral paternalists engaging in an automatized process of notice-and-comment rulemaking using Big Data methods still encounter epistemological problems and the problems associated with radical uncertainty unearthed during the socialist calculation debate and afterwards.

     

THE 'CHILLING EFFECT' OF CONVENTIONAL ARBITRATION: A COUNTEREXAMPLE

In the context of a simple model, it is demonstrated that it is possible for a conventional arbitrator to determine his decision in such a way as to remove the so-called 'chilling effect'. It is shown that an arbitrator adopting the kind of rule envisaged here would be more successful in moderating claims of the negotiators than would a final-offer arbitrator.     

FAIR ALLOCATION OF DISPUTED PROPERTIES

We model problems of allocating disputed properties as generalized exchange economies. Therein, agents have preferences and claims over multiple goods, and the social endowment of each good may not be sufficient to satisfy all individual claims. We focus on market‐based allocation rules that impose a two‐step procedure: assignment of rights based on claims first and voluntary exchange based on the assigned rights afterward. We characterize three focal egalitarian rights‐assignment rules that guarantee that the allocation rules are fair. We apply our results to problems of greenhouse gas emissions and contested water rights.     

Term structure and forward guidance as instruments of monetary policy

This paper studies a simple monetary model with a Ricardian fiscal policy in which equilibria are indeterminate if monetary policy consists solely of a rule for fixing the short-term interest rate. We introduce explicitly into the model the agents’ expectations of inflation which create the indeterminacy and show that there are two types of policies—a term structure rule or a forward guidance rule for the short rate—which lead to determinacy. The first consists in fixing the interest rates on a family of bonds of different maturities as function of realized inflation; the second consists in fixing the short-term interest rate and the expected values of the short-term interest rate for a sequence of periods into the future as a function of realized inflation. If the monetary authority chooses an inflation process that satisfies conditions derived in the paper and applies one of these rules, it anchors agents’ expectations to this process, in the sense that it is the unique inflation process compatible with equilibrium when the interest rates or expected future values of the short rate are those specified by the term structure or forward guidance rule.     

Jointly optimal monetary and fiscal policy rules under liquidity constraints

We study the welfare properties of an economy where both monetary and fiscal policies follow simple rules, and where a subset of agents is liquidity constrained. The welfare benefits of optimizing the fiscal rule are far larger than those of optimizing the monetary rule. The optimized fiscal rule implements strong automatic stabilizers that primarily stabilize the income of liquidity-constrained agents, rather than output. Transfers targeted to liquidity-constrained agents are the preferred fiscal instrument. The optimized monetary rule exhibits super-inertia and a weak inflation response. Optimized simple rules perform as well as the optimal policy under the timeless perspective.     

The Exchange Rate and its Fundamentals in a Complex World

We develop a nonlinear exchange rate model with heterogeneous agents. Some agents adopt a “fundamentalist” forecasting rule, while others use a “chartist” forecasting rule. We show that the model is capable of explaining the empirical puzzles relating to exchange rate movements. In particular, the model explains the “exchange rate determination” and PPP puzzles, the excess volatility, and fat tails in exchange rate returns.     

Modeling non-monotone risk aversion using SAHARA utility functions

We develop a new class of utility functions, SAHARA utility, with the distinguishing feature that it allows absolute risk aversion to be non-monotone and implements the assumption that agents may become less risk averse for very low values of wealth. The class contains the well-known exponential and power utility functions as limiting cases. We investigate the optimal investment problem under SAHARA utility and derive the optimal strategies in an explicit form using dual optimization methods. We also show how SAHARA utility functions extend the class of contingent claims that can be valued using indifference pricing in incomplete markets.     

An Equilibrium Approach to the Aggregation of Beliefs

This paper presents a new answer to the old question of how to aggregate individual beliefs. We construct a model which allows agents to take arbitrage opportunities against the aggregated belief by making contingent claims against the states, and the aggregator (market maker) regulates the probability of states. When all claims from the agents are mutually covered for every realization of the state, an aggregation of individual beliefs is thus obtained. We prove the existence and uniqueness of the equilibrium aggregation, and also show that the aggregate belief lies in the convex hull of individual beliefs. This model allows us to address some important problems such as how individual agent’s attitude toward risk and wealth endowment affect the outcome of the aggregation process, and whether the aggregate belief satisfies the well-known properties like equal treatment.     

Asymmetric parametric division rules

We describe and characterize the family of asymmetric parametric division rules for the adjudication of conflicting claims on a divisible homogeneous good. As part of the characterization, we present two novel axioms which restrict how a division rule indirectly allocates between different versions of the same claimant. We also show that such division rules can alternately be represented as the maximization of an additively separable social welfare function.