Economies with a mean demand function

The present paper shows one way to look at G. Debreu and W. Hildenbrand's conjecture that certain atomless economies have mean demand functions. We conclude within the continuity framework that an economy gives rise ‘in general’ to a continuous mean demand function, and that the class of all atomless economies is ‘big’ in the space of all economies with a continuous mean demand function. The same problems are reconsidered within the framework of a space of differentiable preferences at the end.     

On continuous utility functions derived from demand functions

In the theory of revealed preference and in the approach to integrability theory of Hurwicz and Uzawa certain conditions are proposed implying the existence of a utility function generating the given demand function. This article presents a hypothesis which, under supposition of some well-known axioms of those models, is necessary and sufficient for the existence of a continuous utility function. This hypothesis implies the existence of a utility function u with the property that all of the boundary points of the set $\text{{x|u(x)≧α}}$ for every $\text{α?}\text{R}$ are lower boundary points, being fundamental for the continuity of the utility function.     

Strategy-proofness and population-monotonicity for house allocation problems

We study a simple model of assigning indivisible objects to agents, such as dorm rooms to students, or offices to professors, where each agent receives at most one object and monetary compensations are not possible. For these problems population-monotonicity, which requires that agents are affected by population changes in the same way, is a compelling property because tentative assignments are made in many typical situations, which may have to be revised later to take into account the changing population. We completely describe the allocation rules satisfying population-monotonicity, strategy-proofness, and efficiency. The characterized rules assign the objects by an iterative procedure in which at each step no more than two agents “trade” objects from their hierarchically specified “endowments.”     

Modeling institutional evolution

This paper proposes a formal framework to analyze the process of institutional evolution in relation with economic progress. Institutions have both formal (F) and informal (N) aspects that may exhibit varying processes of change. N is hypothesized to evolve with the level of capital stock, as in learning by doing, whereas F is chosen optimally by a government that maximizes output subject to social and political costs. F and N together define the production technology and affect the income level. Consistent with evidence, simulations of the model's solution reveal that optimum F exhibits a punctuated pattern.     

A continuity property for local price adjustment mechanisms

This paper makes a case that a (local) continuity property is a reasonable one for any local price adjustment mechanism. This property means that if the starting points (i.e., initial prices) of the adjustment process are ‘close' to one another, and if the characteristics of the economies are ‘close' to one another, then, given any price adjustment mechanism, agents should compute equilibria that are ‘close' to one another. Under preferences which satisfy a ‘surjectivity hypothesis', it is shown that the tâtonnement process satisfies this continuity property on a nice subset of the space of all economies. A characterization of these economies for which the tâtonnement process is locally stable is given. Chart logic is a useful way to think about the path dependent property of implied volatility and about the relationship between implied volatility and historical volatility.     

Commodity money equilibrium in a convex trading post economy with transaction costs

Existence and efficiency of general equilibrium with commodity money is investigated in an economy where N   commodities are traded at N(N−1)/2$N(N-1)/2$ commodity-pairwise trading posts. Trade is a resource-using activity recovering transaction costs through the spread between bid (wholesale) and ask (retail) prices. Budget constraints, enforced at each trading post separately, imply demand for a carrier of value between trading posts. Existence of general equilibrium is established under conventional convexity and continuity conditions while structuring the price space to account for distinct bid and ask price ratios. Commodity money flows are identified as the difference between gross and net inter-post trades.     

Simple axioms for countably additive subjective probability

This paper refines Savage’s theory of subjective probability for the case of countably additive beliefs. First, I replace his continuity axioms P6 and P7 with a simple modification of Arrow’s (1970) Monotone Continuity. Second, I relax Savage’s primitives: in my framework, the class of events need not be a σ-algebra, and acts need not have finite or bounded range. By varying the domains of acts and events, I obtain a unique extension of preference that parallels Caratheodory’s unique extension of probability measures. Aside from subjective expected utility, I characterize exponential time discounting in a setting with continuous time and an arbitrary consumption set.     

A numerical representation of preferences with intransitive indifference

It is shown that, under certain conditions on a preference relation on a subset X of R^m, there exist real-valued functions u and v on X such that x is preferred to y if and only if u(x)>v(y). This generalises the familiar representation of preferences by a utility function in the case where the preference and indifference relations are transitive. The continuity of the functions u and v is also discussed.     

On properties of division rules lifted by bilateral consistency

We consider the problem of adjudicating conflicting claims in the context of a variable population. A property of rules is “lifted” if whenever a rule satisfies it in the two-claimant case, and the rule is bilaterally consistent, it satisfies it for any number of claimants. We identify a number of properties that are lifted, such as equal treatment of equals, resource monotonicity, composition down and composition up, and show that continuity, anonymity and self-duality are not lifted. However, each of these three properties is lifted if the rule is resource monotonic.     

Weakened WARP and top-cycle choice rules

We propose the following weakened version of WARP: if the decision maker selects an alternative x and rejects another alternative y in some context, he cannot select y and reject x in another context. This axiom is consistent with cyclic choices. It is necessary and sufficient for the choice from every subset A of a (finite) universal set X to coincide with the weak upper-contour set of the transitive closure of some fixed complete relation at some alternative in A. Adding further simple axioms forces the choice from each subset to coincide with the top cycle (in that subset) of some fixed tournament over the universal set.     

Spatial pillage game

A pillage game is a coalitional game as a model of Hobbesian anarchy. The spatial pillage game introduces a spatial feature into the pillage game. Players are located in regions and can travel from one region to another. The players can form a coalition and combine their power only within their destination regions, which limits the exertion of the power of each coalition. Under this spatial restriction, a coalition can pillage less powerful coalitions without any cost. The feasibility of pillages between coalitions determines the dominance relation that defines stable states in which powers among the players are endogenously balanced. With the spatial restriction, the set of stable states changes. However, if the players have forecasting ability, then the set of stable states does not change with the spatial restriction. Core, stable set, and farsighted core are adopted as alternative solution concepts.     

Note on the existence and modulus of continuity of the {\textit{SLE}}_8 curve

We review one method for estimating the modulus of continuity of a Schramm–Loewner evolution (SLE) curve in terms of the inverse Loewner map. Then we prove estimates about the distribution of the inverse Loewner map, which underpin the difficulty in bounding the modulus of continuity of SLE for $\kappa =8$ . The main idea in the proof of these estimates is applying the Girsanov theorem to reduce the problem to estimates about one-dimensional Brownian motion.     

Predicting loss given default (LGD) for residential mortgage loans: A two-stage model and empirical evidence for UK bank data

With the implementation of the Basel II regulatory framework, it became increasingly important for financial institutions to develop accurate loss models. This work investigates the loss given default (LGD) of mortgage loans using a large set of recovery data of residential mortgage defaults from a major UK bank. A Probability of Repossession Model and a Haircut Model are developed and then combined to give an expected loss percentage. We find that the Probability of Repossession Model should consist of more than just the commonly used loan-to-value ratio, and that the estimation of LGD benefits from the Haircut Model, which predicts the discount which the sale price of a repossessed property may undergo. This two-stage LGD model is shown to perform better than a single-stage LGD model (which models LGD directly from loan and collateral characteristics), as it achieves a better R² value and matches the distribution of the observed LGD more accurately.     

Informing national security policy by modeling adversarial inducement and its governance

The distinction between peace and conflict in contemporary international relations is no longer well-defined. Leveraging modern technology, hostile action below the threshold of war has become increasingly effective. The objective of such aggression is often the influence of opinions, emotions, and, ultimately, the decisions of a nation's citizenry. This work presents two new game theoretic frameworks, denoted as prospect games and regulated prospect games, to inform defensive policy against these threats. These frameworks respectively model (a) the interactions of competing entities influencing a populace and (b) the preemptive actions of a regulating agent to alter such a framework. Prospect games and regulated prospect games are designed to be adaptable, depending on the assumed nature of persuaders' interactions and their rationality. The contributions herein are a modeling framework for competitive influence operations under a common set of assumptions, model variants that respectively correspond to scenario-specific modifications of selected assumptions, the illustration of practical solution methods for the suite of models, and a demonstration on a representative scenario with the ultimate goal of providing a quantifiable, tractable, and rigorous framework upon which national policies defending against competitive influence can be identified.     

An axiomatization of the core of cooperative games without side payments

Let M be a set of m players, m≧3, and let Γ be the set of all (finite) games (without side payments) that have a non-empty core. When M is finite, the following four (independent) axioms fully characterize the core on Γ: (i) non-emptiness, (ii) individual rationality, (iii) the reduced game property, and (iv) the converse reduced game property. If M is infinite, then the converse reduced game property is redundant.     

Uniform allocation and reallocation revisited

Thomson (1995a) proved that the uniform allocation rule is the only allocation rule for allocation economies with single-peaked preferences that satisfies Pareto efficiency, no-envy,one-sided population-monotonicity, and replication-invariance on a restricted domain of single-peaked preferences. We prove that this result also holds on the unrestricted domain of single-peaked preferences. Next, replacing one-sided population-monotonicity by one-sided replacement-domination yields another characterization of the uniform allocation rule, Thomson (1997a). We show how this result can be extended to the more general framework of reallocation economies with individual endowments and single-peaked preferences. Following Thomson (1995b) we present allocation and reallocation economies in a unified framework of open economies. Received: 20 February 1999 / Accepted: 15 February 2000     

Quest for appropriate overcapacity in the fisheries industry

The effective management of natural resources is a critical issue that concerns many people with differing interests. This paper examines aspects of overcapacity and optimal capacity within fisheries by accounting for multiple objectives. Overcapacity arises when a fishing fleet is capable of producing more than what is demanded at the industry level, or allowed by a regulatory framework. The presence of multiple objectives within fisheries management is most often an unavoidable reality, where the objectives determine what level of overcapacity is considered optimal. A two-stage model is suggested that can produce information for management in terms of tradeoffs, policy frontiers, objective values and optimal fleet structure. In the first stage, an output-based Data Envelopment Analysis (DEA) model is applied. Efficiency is evaluated and production units transformed such that they use technologically efficient inputs and produce at their full potential. In the second stage, these transformed units are included in an aggregate industry model formulated as a multi-objective optimization program. The model provides information for managers in terms of tradeoffs, policy frontiers, objective values, and optimal fleet structure (by generating Pareto optimal solutions). The proposed model has then been applied to the Danish commercial fishing fleet.     

Strictly monotonic preferences on continuum of goods commodity spaces

We consider a set K of differentiated commodities. A preference relation on the set of consumption plans is strictly monotonic whenever to consume more of at least one commodity is more preferred. It is an easy task to find examples of strictly monotonic preference relations when K   is finite or countable. However, it is not easy for spaces like ?^∞([0,1])${?}^{\infty }([0\text{,}1])$, the space of bounded functions on the unit interval.     

How similar are they? rethinking electoral congruence

Electoral continuity and discontinuity have been a staple of voting research for decades. Most researchers have employed Pearson’s r as a measure of congruence between two electoral outcomes across a set of geographic units. This paper argues that that practice should be abandoned. The correlation coefficient is a measure of linearity, not similarity, and is almost always the wrong measure. The paper recommends other quantities that better accord with what researchers usually mean by electoral persistence. Replications of prior studies in American and comparative politics demonstrate that the consequences of using r when it is inappropriate can be stark. In some cases what we think are continuities are actually discontinuities.     

Continuity and incentive compatibility in cardinal mechanisms

In models without transfers, we show that every cardinal incentive compatible voting mechanism satisfying a continuity condition, can only take ordinal, but not cardinal information into account. Our results apply to many standard models in mechanism design without transfers, including the standard voting models with any domain restrictions.