Interacting mechanisms of time inconsistency

We interact two prominent behavioral mechanisms of time inconsistency that have been used to study inadequate saving: hyperbolic discounting and short-term planning. Hyperbolic discounting is a conventional way to model impulsive decision making, and short planning horizons have been used to represent myopia. One might expect that interacting both mechanisms within the same model would compound the inadequacy of saving. However, our key finding takes the form of a paradox: hyperbolic discounting does not affect consumption and saving allocations if the planning horizon is short and fixed, although it will affect allocations if the planning horizon is equal to the remaining life span. We demonstrate analytically that this finding is robust to the shape of the disposable income path, to the coarseness of the time grid, and to alternative forms of the period utility function.     

A theory of policy differentiation in single issue electoral politics

Voter preferences are characterized by a parameter s (say, income) distributed on a set S according to a probability measure F. There is a single issue (say, a tax rate) whose level, b, is to be politically decided. There are two parties, each of which is a perfect agent of some constituency of voters, voters with a given value of s. An equilibrium of the electoral game is a pair of policies, b ₁ and b ₂, proposed by the two parties, such that b _i maximizes the expected utility of the voters whom party i represents, given the policy proposed by the opposition. Under reasonable assumptions, the unique electoral equilibrium consists in both parties proposing the favorite policy of the median voter. What theory can explain why, historically, we observe electoral equilibria where the ‘right’ and ‘left’ parties propose different policies? Uncertainty concerning the distribution of voters is introduced. Let {F(t)} _{t ε T} be a class of probability measures on S; all voters and parties share a common prior that the distribution of t is described by a probability measure H on T. If H has finite support, there is in general no electoral equilibrium. However, if H is continuous, then electoral equilibrium generally exists, and in equilibrium the parties propose different policies. Convergence of equilibrium to median voter politics is proved as uncertainty about the distribution of voter traits becomes small.     

The equivalence of the cost share equilibria and the core of a voting game in a public goods economy

We consider a social situation where individuals choose one or some alternative(s) from a set of feasible alternatives. When one alternative is socially chosen, each individual must share the cost for it according to an exogenously given sharing rule. Individuals are allowed to collude among themselves through money transfers. As the mechanism of choosing a social alternative, we consider the cost share equilibrium and a voting game. The cost share equilibrium is an allocation where each individual maximizes his/her utility independently and where unanimity is still maintained. We will show the equivalence between the set of all equilibrium allocations and the core of the voting game with compensation.I would like to thank Professors Mamoru Kaneko, Kotaro Suzumura, William Thomson, Mikio Nakayama, Hiroo Sasaki, Mr. Ken-ichi Shimomura and anonymous referees for their many useful suggestions and comments. I also acknowledge grammatical suggestions of Mr. Ronald M. Siani.     

Dynamic contests with resource constraints

We study a dynamic contest between two players who compete against each other in $n$ different stages. The players have winning values for each stage of the contest that may vary across the stages as well as heterogeneous resource budgets that decrease from a given stage to the next proportionally to the resources allocated in that stage. We characterize a subgame perfect equilibrium of this dynamic contest and show that when the winning value is equal between the stages, the players’ resource allocations are weakly decreasing over the stages. We also study the effect of several distributions of winning values on the players’ resource allocations. We show both the distribution of winning values that balances the players’ resource allocations and the distribution of winning values that maximizes the players’ total resource allocations.     

Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities

This paper studies the existence of Pareto optimal, envy-free allocations of a heterogeneous, divisible commodity for a finite number of individuals. We model the commodity as a measurable space and make no convexity assumptions on the preferences of individuals. We show that if the utility function of each individual is uniformly continuous and strictly monotonic with respect to set inclusion, and if the partition matrix range of the utility functions is closed, a Pareto optimal envy-free partition exists. This result follows from the existence of Pareto optimal envy-free allocations in an extended version of the original allocation problem.     

Existence and Nash implementation of efficient sharing rules for a commonly owned technology

Suppose that a group of individuals owns collectively a technology which produces a consumption good by means of a (possibly heterogeneous) input. A sharing rule associates input contributions with a vector of consumptions that are technologically feasible. We show that the set of allocations obtained by any continuous sharing rule contains Pareto efficient allocations. We also present a mechanism that implements in Nash equilibrium the Pareto efficient allocations contained in an arbitrary sharing rule. Received: 29 June 1998/Accepted: 15 November 2000     

Generic efficiency and collusion-proofness in exchange economies

The purpose of this paper is to study the kind of efficient allocations that can be achieved in exchange economies with asymmetric information, by means of a decentralized mechanism robust to coalitional, strategic deviations. To this end, we define a new strategic equilibrium concept – called strong collusion-proof contract – designed to characterize stable communication agreements in games with differential information against non-binding, self-enforcing and incentive compatible deviations by coalitions. We then construct a strategic market mechanism which, for quasi-linear economies, is such that its strong collusion-proof contracts generically induce the incentive compatible interim efficient allocations. Moreover, we show that these allocations can be achieved by strong collusion-proof contracts. We show that the internally consistent extension of the strong collusion-proof contracts generically yields the same set of efficient allocations. Received: 22 January 2001/Accepted: 15 April 2002 RID="*" ID="*"  This author was working at CORE when this paper was written. We wish to thank Claude d'Aspremont, David Martimort, Jean-Fran?ois Mertens and Heracles Polemarchakis for helpful comments on an earlier version. The usual disclaimer applies.     

Implementation in generic environments

In this paper, we study implementation in “economic environments”. It is shown that there is a dense subset of the set of preference profiles such that given an arbitrary social choice function, f, and ε>0, there exists another social choice function, f _ε, within ε of f uniformly and implementable in Nash equilibrium on the dense subset.     

Path independent choice and the ranking of opportunity sets

The indirect utility principle provides an instrumentalist basis for ranking opportunity sets, given an underlying preference ranking on alternatives. Opportunity set A is weakly preferred to B if A includes at least one preference-maximising element from $A\cup B$ . We introduce the Plott consistency principle as a natural extension of this logic to decision-makers who choose amongst alternatives according to a path independent choice function. Such choice functions need not be rationalisable by a preference order. Plott consistency requires that A is an acceptable choice from $\left\{ A, B\right\} $ if A includes at least one element from the set of acceptable choices from $A\cup B$ . We explore necessary and sufficient conditions (imposed on a choice function defined on collections of opportunity sets) for Plott consistency.     

Social choice in economic environments with dimensional variation

An argument for welfarist social evaluation is presented that replaces the independence axiom with a consistency axiom for social-evaluation functionals in economic environments. This axiom (consistency across dimension or COAD) requires that, if two allocations contain suballocations in common, and if individual utility functions are projected down to the smaller economy where allocations change, then these small allocations must be ranked in the same way that their ancestral allocations were.The basic result is applied to different information environments and a variety of ethical axioms appropriate to economic environments is investigated.We are indebted to Charles Blackorby, Erwin Diewert, Ed Morey, Bill Schworm and John Weymark for helpful discussions, and to the Social Sciences and Humanities Research Council, the Killiam Foundation and the National Science Foundation, for research support.     

An algorithm for envy-free allocations in an economy with indivisible objects and money

This paper studies envy-free allocations for economies with indivisible objects, quasi-linear utility functions, and an amount of money. We give a polynomially bounded algorithm for finding envy-free allocations. Connectedness of envy-graphs, which are used in the algorithm, characterizes the extreme points of the polytopes of sidepayments corresponding with envy-free allocations. Received: 22 October 1997/Accepted: 19 January 1999     

The ordinal egalitarian bargaining solution for finite choice sets

Rubinstein et al. (Econometrica 60:1171–1186, 1992) introduced the Ordinal Nash Bargaining Solution. They prove that Pareto optimality, ordinal invariance, ordinal symmetry, and IIA characterize this solution. A feature of their work is that attention is restricted to a domain of social choice problems with an infinite set of basic allocations. We introduce an alternative approach to solving finite social choice problems using a new notion called the Ordinal Egalitarian (OE) bargaining solution. This suggests the middle ranked allocation (or a lottery over the two middle ranked allocations) of the Pareto set as an outcome. We show that the OE solution is characterized by weak credible optimality, ordinal symmetry and independence of redundant alternatives. We conclude by arguing that what allows us to make progress on this problem is that with finite choice sets, the counting metric is a natural and fully ordinal way to measure gains and losses to agents seeking to solve bargaining problems.     

Axiomatization of ratio equilibria in public good economies

Using consistency properties, we characterize the cost-sharing scheme arising from the ratio equilibrium concept for economies with public goods. The characterization turns out to be surprisingly simple and direct. In contrast to most axiomatic characterizations based on reduced games and consistency properties, our characterization requires that in the reduced game, the players take as given the proportions of the costs paid by the members of the complementary player set, rather than their utility levels. Received: 4 July 1996/Accepted: 28 March 2001     

Effects of age and physical activity on response speed in knee flexor and extensor muscles

This study aims to determine the normalized response speed (V _rn) in vastus lateralis (VL) and biceps femoris (BF) muscles in different age groups using tensiomyography. Eighty-four male subjects were divided into four age groups: teenage subjects (T); undergraduate students (U), adult subjects (A), and the elderly group (E). Differences in V _rn were observed between E and T (p?=?0.000), E and U (p?=?0.000), and E and A (p?=?0.018) for right VL and between E and T (p?<?0.000) and U (p?=?0.003) for left VL; between T and U (p?=?0.010) and A (p?=?0.000) for right VL, and A (p?=?0.004) for left VL. V _rn in the BF displayed different behavior from that of the VL, increasing moderately or stabilizing and declining slightly in E, in right leg (p?=?0.020). The data obtained highlighted a decline in V _rn for the VL in both legs with increasing age and, declines in BF response speed were observed only in E.     

Money-egalitarian-equivalent and gain-maximin allocations of indivisible items with monetary compensation

Suppose that a certain quantity M of money and a finite number of indivisible items are to be distributed among n people, all of whom have equal claims on the whole. Different allocations are presented using various criteria of fairness in the special case where each player's utility function is additively separable. An allocation is “money-egalitarian-equivalent” (MEE) if each player's monetary valuation of his or her bundle is a fixed constant. We show that there is an essentially unique allocation that is MEE and Pareto-optimal; it is also envy-free. Alternatively, the “gain” of a player may be defined as the difference between how the player evaluates his bundle and an exact nth part of the whole according to his numerical evaluation of the whole. A “gain-maximin” criterion would maximize the minimum gain obtained by any player. We show that Knaster's procedure finds an allocation which is optimal under the gain-maximin criterion. That allocation is not necessarily envy-free, so we also find the envy-free allocation that is optimal under the gain-maximin criterion among all envy-free allocations. It turns out that, even though there exist allocations that are simultaneously envy-free and Pareto-optimal, this optimal allocation may fail to be Pareto-optimal, and it may also violate monotonicity criteria. Received: 30 September 1996/Accepted: 6 March 2002 The author would like to thank Professor William Thomson for a discussion on this subject; and he would like to thank the anonymous referees, who made many substantive suggestions for improving this paper – shortening it, streamlining the arguments, improving the terminology, making further ties with the literature, and improving the exposition.     

Aggregation of smooth preferences

Suppose p is a smooth preference profile (for a society, N) belonging to a domain P ^N . Let σ be a voting rule, and σ(p)(x) be the set of alternatives in the space, W, which is preferred to x. The equilibrium E(σ(p)) is the set {x∈W:σ(p)(x) is empty}. A sufficient condition for existence of E(σ(p)) when p is convex is that a “dual”, or generalized gradient, dσ(p)(x), is non-empty at all x. Under certain conditions the dual “field”, dσ(p), admits a “social gradient field”Γ(p). Γ is called an “aggregator” on the domain P ^N if Γ is continuous for all p in P ^N . It is shown here that the “minmax” voting rule, σ, admits an aggregator when P ^N is the set of smooth, convex preference profiles (on a compact, convex topological vector space, W) and P ^N is endowed with a C ¹-topology. An aggregator can also be constructed on a domain of smooth, non-convex preferences when W is the compact interval. The construction of an aggregator for a general political economy is also discussed. Some remarks are addressed to the relationship between these results and the Chichilnisky-Heal theorem on the non-existence of a preference aggregator when P ^N is not contractible. Received: 4 July 1995 / Accepted: 26 August 1996     

Probabilistic allocation rules and single-dipped preferences

We consider the problem of allocating an infinitely divisible endowment among a group of agents with single-dipped preferences. A probabilistic allocation rule assigns a probability distribution over the set of possible allocations to every preference profile. We discuss characterizations of the classes of Pareto-optimal and strategy-proof probabilistic rules which satisfy in addition replacement-domination or no-envy. Interestingly, these results also apply to problems of allocating finitely many identical indivisible objects – to probabilistic and to deterministic allocation. Received: 23 November 1998/Accepted: 20 October 2000     

Nest predators,but not nest survival,differ between adjacent urban habitats

Growing human populations make it imperative for ecologists to identify strategies to conserve biodiversity in human-dominated landscapes, such as cities. Effects of urbanization on birds are particularly well-studied, but questions remain regarding the best conservation approaches. Debate about the relative utility of focusing conservation efforts on nature reserves versus developed lands has focused largely on comparing species abundance or presence, with few studies addressing underlying behavioral or demographic mechanisms. Here we evaluated differences in avian reproductive success in nature reserves and matrix habitats to test the assumption that nest predation is lower within areas protected from development. Specifically, we investigated 1) whether nest survival differed in replicated pairs of forest parks and residential neighborhoods and 2) whether differences in nest survival were associated with changes in which species most frequently depredated nests. From April–August 2007–2014, we monitored nests of two native birds, American robin (Turdus migratorius) and northern cardinal (Cardinalis cardinalis), and video-documented nest predators in paired forest-matrix habitats in the Columbus, Ohio metropolitan area. We found similar rates of nest survival in the two habitats for both robins (Χ²₁?=?0.715, p?=?0.398, n?=?741 nests) and cardinals (Χ²₁?=?0.926, p?=?0.336, n?=?1156 nests), but interactions between predators and prey differed. In particular, domestic cats (Felis catus) were over five times as likely to depredate cardinal nests in matrix habitats versus forest parks (Χ²₁?=?7.24, simulated p?=?0.010; n_forest?=?3, n_matrix?=?7). Our results suggest that at least in some circumstances, nest success of native birds may be equivalent between nature reserves and adjacent residential matrix habitats, and thus residential neighborhoods may contribute positively to bird conservation in urban landscapes.     

Alternate Definitions of the Uncovered Set and Their Implications

Different definitions of the uncovered set are commonly, and often interchangeably, used in the literature. If we assume individual preferences are strict over all alternatives, these definitions are equivalent. However, if one or more voters are indifferent between alternatives these definitions may not yield the same uncovered set. This note examines how these definitions differ in a distributive setting, where each voter can be indifferent between any number of alternatives. I show that, defined one way, the uncovered set is equal to the set of Pareto allocations that give over half the voters a strictly positive payoff, while alternate definitions yield an uncovered set that is equal to the entire Pareto set. These results highlight a small error in Epstein (Soc Choice Welf 15, 81–93, 1998) in which the author characterizes the uncovered set for a different definition of covering than claimed.