How to Cope with Division Problems under Interval Uncertainty of Claims?

The paper deals with division situations where individual claims can vary within closed intervals.Uncertainty of claims is removed by compromising in a consistent way the upper and lower bounds of the claim intervals.Deterministic division problems with compromise claims are then considered and classical division rules from the bankruptcy literature are used to generate several procedures leading to e .cient and reasonable rules for division problems under interval uncertainty of claims.uncertainty;claims;division problems

Cooperation under Interval Uncertainty

Classification: JEL code C71Cooperative game theory;Interval uncertainty;Core;Value;Balancedness

Cores and Stable Sets for Interval-Valued Games

In this paper, interval-type solution concepts for interval-valued cooperative games like the interval core, the interval dominance core and stable sets are introduced and studied. The notion of I-balancedness is introduced, and it is proved that the interval core of an interval-valued cooperative game is nonempty if and only if the game is I-balanced. Relations between the interval core, the dominance core and stable sets of an interval-valued game are established.cooperative games;interval games;the core;the dominance core;stable sets

Cake Cutting Algorithms for Piecewise Constant and Piecewise Uniform Valuations

Cake cutting is one of the most fundamental settings in fair division and mechanism design without money. In this paper, we consider different levels of three fundamental goals in cake cutting: fairness, Pareto optimality, and strategyproofness. In particular, we present robust versions of envy-freeness and proportionality that are not only stronger than their standard counter-parts but also have less information requirements. We then focus on cake cutting with piecewise constant valuations and present three desirable algorithms: CCEA (Controlled Cake Eating Algorithm), MEA (Market Equilibrium Algorithm) and CSD (Constrained Serial Dictatorship). CCEA is polynomial-time, robust envy-free, and non-wasteful. It relies on parametric network flows and recent generalizations of the probabilistic serial algorithm. For the subdomain of piecewise uniform valuations, we show that it is also group-strategyproof. Then, we show that there exists an algorithm (MEA) that is polynomial-time, envy-free, proportional, and Pareto optimal. MEA is based on computing a market-based equilibrium via a convex program and relies on the results of Reijnierse and Potters [24] and Devanur et al. [15]. Moreover, we show that MEA and CCEA are equivalent to mechanism 1 of Chen et. al. [12] for piecewise uniform valuations. We then present an algorithm CSD and a way to implement it via randomization that satisfies strategyproofness in expectation, robust proportionality, and unanimity for piecewise constant valuations. For the case of two agents, it is robust envy-free, robust proportional, strategyproof, and polynomial-time. Many of our results extend to more general settings in cake cutting that allow for variable claims and initial endowments. We also show a few impossibility results to complement our algorithms.Comment: 39 page

Equity in health care financing: The case of Malaysia

Background: Equitable financing is a key objective of health care systems. Its importance is evidenced in policy documents, policy statements, the work of health economists and policy analysts. The conventional categorisations of finance sources for health care are taxation, social health insurance, private health insurance and out-of-pocket payments. There are nonetheless increasing variations in the finance sources used to fund health care. An understanding of the equity implications would help policy makers in achieving equitable financing. Objective: The primary purpose of this paper was to comprehensively assess the equity of health care financing in Malaysia, which represents a new country context for the quantitative techniques used. The paper evaluated each of the five financing sources (direct taxes, indirect taxes, contributions to Employee Provident Fund and Social Security Organization, private insurance and out-of-pocket payments) independently, and subsequently by combined the financing sources to evaluate the whole financing system. Methods: Cross-sectional analyses were performed on the Household Expenditure Survey Malaysia 1998/99, using Stata statistical software package. In order to assess inequality, progressivity of each finance sources and the whole financing system was measured by Kakwani's progressivity index. Results: Results showed that Malaysia's predominantly tax-financed system was slightly progressive with a Kakwani's progressivity index of 0.186. The net progressive effect was produced by four progressive finance sources (in the decreasing order of direct taxes, private insurance premiums, out-of-pocket payments, contributions to EPF and SOCSO) and a regressive finance source (indirect taxes). Conclusion: Malaysia's two tier health system, of a heavily subsidised public sector and a user charged private sector, has produced a progressive health financing system. The case of Malaysia exemplifies that policy makers can gain an in depth understanding of the equity impact, in order to help shape health financing strategies for the nation

Some neglected axioms in fair division

Conditions one might impose on fair allocation procedures are introduced. Nondiscrimination requires that agents share an item in proportion to their entitlements if they receive nothing else. The "price" procedures of Pratt (2007), including the Nash bargaining procedure, satisfy this. Other prominent efficient procedures do not. In two-agent problems, reducing the feasible set between the solution and one agent's maximum point increases the utility cost to that agent of providing any given utility gain to the other and is equivalent to decreasing the dispersion of the latter's values for the items he does not receive without changing their total. One-agent monotonnicity requires that such a change should not hurt the first agent, limited monotonicity that the solution should not change. For prices, the former implies convexity in the smaller of the two valuations, the latter linearity. In either case, the price is at least their average and hence spiteful.Fair division, efficient allocation, nondiscrimination axiom, monotonicity axioms, envy-free, spite, bargaining solutions.

Dynamic Disappointment Aversion: Don't Tell Me Anything Until You Know For Sure

We show that for a disappointment-averse decision maker, splitting a lottery into several stages reduces its value. To do this, we extend Gul.s (1991) model of disappointment aversion into a dynamic setting while keeping its basic characteristics intact. The result depends solely on the sign of the coefficient of disappointment aversion. It can help explain why people often buy periodic insurance for moderately priced objects, such as electrical appliances and cellular phones, at much more than the actuarially fair rate.Disappointment aversion, recursive preferences, compound lotteries

Bargaining under Incomplete Information, Fairness, and the Hold-Up Problem

In the hold-up problem incomplete contracts cause the proceeds of relation specific investments to be allocated by ex-post bargaining. The present paper investigates the efficiency of incomplete contracts if individuals have heterogeneous preferences implying heterogeneous bargaining behavior and - equally important - preferences are private information. As the sunk investment costs can thus potentially signal preferences, they can influence beliefs and consequently bargaining outcomes. The necessities of signalling are shown to generate very strong investment incentives. These incentives are based on the desire not to reveal information that is unfavorable in the ensuing bargaining. After finding all perfect Bayesian equilibria in pure strategies, the paper derives the necessary and sufficient conditions under which it is optimal to invest and trade efficiently