An axiomatic justification of mediation in bankruptcy problems.

This paper provides a natural way of reaching an agreement between two prominent proposals in a bankruptcy problem. Particularly, using the fact that such problems can be faced from two different points of views, awards and losses, we justify the average of any pair of dual bankruptcy rules through the definition a double recursive process. Finally, by considering three posible sets of equity principles that a particular society may agree on, we retrieve the average of old and well known bankruptcy rules, the Constrained Equal Awards and the Constrained Equal Losses rules, Piniles’ rule and its dual rule, and the Constrained Egalitarian rule and its dual rule. Keywords: Bankruptcy problems, Midpoint, Bounds, Duality, Recursivity. JEL classification: C71, D63, D71.

A way to play bankruptcy problems.

The commitment among agents has always been a difficult task, especially when they have to decide how to distribute the available amount of a scarce resource among all. On the one hand, there are a multiplicity of possible ways for assigning the available amount; and, on the other hand, each agent is going to propose that distribution which provides her the highest possible award. In this paper, with the purpose of making this agreement easier, firstly we use two different sets of basic properties, called Commonly Accepted Equity Principles, to delimit what agents can propose as reasonable allocations. Secondly, we extend the results obtained by Chun (1989) and Herrero (2003), obtaining new characterizations of old and well known bankruptcy rules. Finally, using the fact that bankruptcy problems can be analyzed from awards and losses, we define a mechanism which provides a new justification of the convex combinations of bankruptcy rules. Keywords: Bankruptcy problems, Unanimous Concessions procedure, Diminishing Claims mechanism, Piniles’ rule, Constrained Egalitarian rule. JEL classification: C71, D63, D71.

A Proportional Approach to Bankruptcy Problems with a guaranteed minimum

In a distribution problem, and specfii cally in bankruptcy issues, the Proportional (P) and the Egalitarian (EA) divisions are two of the most popular ways to resolve the conflict. The Constrained Equal Awards rule (CEA) is introduced in bankruptcy literature to ensure that no agent receives more than her claim, a problem that can arise when using the egalitarian division. We propose an alternative modi cation, by using a convex combination of P and EA. The recursive application of this new rule finishes at the CEA rule. Our solution concept ensures a minimum amount to each agent, and distributes the remaining estate in a proportional way. Keywords: Bankruptcy problems, Proportional rule, Equal Awards, Convex combination of rules, Lorenz dominance. JEL classi fication: C71, D63, D71.

Solidarity and uniform rules in bankruptcy problems

The idea of ensuring a guarantee (a minimum amount of the resources) to each agent has recently acquired great relevance, in both social and politi- cal terms. Furthermore, the notion of Solidarity has been treated frequently in redistribution problems to establish that any increment of the resources should be equally distributed taking into account some relevant characteris- tics. In this paper, we combine these two general concepts, guarantee and solidarity, to characterize the uniform rules in bankruptcy problems (Con- strained Equal Awards and Constrained Equal Losses rules). Keywords: Constrained Equal Awards, Constrained Equal Losses, Lower bounds, Bankruptcy problems, Solidarity. JEL classification: C71, D63, D71.

A note on discrete claims problems

In this note, we consider claims problems with indivisible goods. Specifically, by applying recursively the P-rights lower bound (Jiménez-Gómez and Marco-Gil (2008)), we ensure the fulfillment of Weak Order Preservation, considered by many authors as a minimal requirement of fairness. Moreover, we retrieve the Discrete Constrained Equal Losses and the Discrete Constrained Equal Awards rules (Herrero and Martíınez (2008)). Finally, by the recursive double imposition of a lower and an upper bound, we obtain the average between them. Keywords: Claims problems, Indivisibilities, Order Preservation, Constrained Egalitarian rules, Midpoint. JEL classification: C71, D63, D71.

Rationing problems with payoff thresholds

An extension of the standard rationing model is introduced. Agents are not only identi fied by their respective claims over some amount of a scarce resource, but also by some payoff thresholds. These thresholds introduce exogenous differences among agents (full or partial priority, past allocations, past debts, ...) that may influence the final distribution. Within this framework we provide generalizations of the constrained equal awards rule and the constrained equal losses rule. We show that these generalized rules are dual from each other. We characterize the generalization of the equal awards rule by using the properties of consistency, path-independence and compensated exemption. Finally, we use the duality between rules to characterize the generalization of the equal losses solution.

Chaotic dynamics in credit constrained emerging economies

This paper analyzes the role of financial development as a source of endogenous instability in small open economies. By assuming that firms face credit constraints, our model displays a complex dynamic behavior for intermediate values of the parameter representing the level of financial development of the economy. The basic implication of our model is that economies experiencing a process of financial development are more unstable than both very underdeveloped and very developed economies. Our instability concept means that small shocks have a persistent effect on the long run behavior of the model and also that economies can exhibit cycles with a very high period or even chaotic dynamic patterns.

Resource-monotonicity for house allocation problems

We study a simple model of assigning indivisible objects (e.g., houses, jobs, offices, etc.) to agents. Each agent receives at most one object and monetary compensations are not possible. We completely describe all rules satisfying efficiency and resource-monotonicity. The characterized rules assign the objects in a sequence of steps such that at each step there is either a dictator or two agents "trade" objects from their hierarchically specified "endowments."

Environmental management problems, future generations and social decisions

The decisions of many individuals and social groups, taking according to well-defined objectives, are causing serious social and environmental problems, in spite of following the dictates of economic rationality. There are many examples of serious problems for which there are not yet appropriate solutions, such as management of scarce natural resources including aquifer water or the distribution of space among incompatible uses. In order to solve these problems, the paper first characterizes the resources and goods involved from an economic perspective. Then, for each case, the paper notes that there is a serious divergence between individual and collective interests and, where possible, it designs the procedure for solving the conflict of interests. With this procedure, the real opportunities for the application of economic theory are shown, and especially the theory on collective goods and externalities. The limitations of conventional economic analysis are shown and the opportunity to correct the shortfalls is examined. Many environmental problems, such as climate change, have an impact on different generations that do not participate in present decisions. The paper shows that for these cases, the solutions suggested by economic theory are not valid. Furthermore, conventional methods of economic valuation (which usually help decision-makers) are unable to account for the existence of different generations and tend to obviate long-term impacts. The paper analyzes how economic valuation methods could account for the costs and benefits enjoyed by present and future generations. The paper studies an appropriate consideration of preferences for future consumption and the incorporation of sustainability as a requirement in social decisions, which implies not only more efficiency but also a fairer distribution between generations than the one implied by conventional economic analysis.

Inverse Problems for multiple invariant curves

Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals are of special interest. In the present paper we solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. In particular we prove, in this generic scenario, that the existence of a Darboux integrating factor implies Darboux integrability. Furthermore we construct examples where the genericity assumption does not hold and indicate that the situation is different for these.

Constrained school choice

Recently, several school districts in the US have adopted or consider adopting the Student-Optimal Stable Mechanism or the Top Trading Cycles Mechanism to assign children to public schools. There is clear evidence that for school districts that employ (variants of) the so-called Boston Mechanism the transition would lead to efficiency gains. The first two mechanisms are strategy-proof, but in practice student assignment procedures impede students to submit a preference list that contains all their acceptable schools. Therefore, any desirable property of the mechanisms is likely toget distorted. We study the non trivial preference revelation game where students can only declare up to a fixed number (quota) of schools to be acceptable. We focus on the stability of the Nash equilibrium outcomes. Our main results identify rather stringent necessary and sufficient conditions on the priorities to guaranteestability. This stands in sharp contrast with the Boston Mechanism which yields stable Nash equilibrium outcomes, independently of the quota. Hence, the transition to any of the two mechanisms is likely to come with a higher risk that students seek legal actionas lower priority students may occupy more preferred schools.

The Evolution of roommate networks: a comment on Jackson and Watts JET (2002)

We extend Jackson and Watts's (2002) result on the coincidence of S-stochastically stable and core stable networks from marriage problems to roommate problems. In particular, we show that the existence of a side-optimal core stable network, on which the proof of Jackson and Watts (2002) hinges, is not crucial for their result.