Passing the Buck On the acceptance of responsibility

In the Passing the Buck game, the n members of a group decide in a given order whether or not to incur costs so that they can fix a certain problem for the benefit of the group. Passing the Buck means that one relies on the service of a successor. The decision is influenced by social preferences and by strategic considerations. We derive three main conclusions from experiments with n=3 and n=4. (i) The unique perfect Baysian equilibrium of the Passing the Buck game with incomplete information about the preferences of other players generally fits the data, however with two interesting exceptions. (ii) Backward induction breaks down if it requires more than two steps, i.e., for the first player in the game with n=4. (iii) Making one of the members of the group an “expert” who alone is competent to fix the problem is connected with a change of social preferences.     

Pure exchange equilibrium of dynamic economic models

This paper studies competitive equilibrium over time of a one good model in which the agents are members of a population which grows at a constant rate. Each agent lives for n periods and in the i-th period of his life receives an endowment of e_i units of goods. Goods can neither be produced nor stored. The model is thus the n-period generalization of the two- and three-period models studied by Samuelson in [4]. We seek to ascertain the structure of the time paths of consumption in these models. Our results can be summarized roughly as follows: In general, there will exist two kinds of steady state paths, (i) golden rule paths in which the rate of interest equals the growth rate of population and (ii) “balanced” paths in which the aggregate assets or indebtedness of the society as a whole is zero (a fundamental fact about dynamic models is that it is possible for aggregate debt not to equal aggregate credit as it must in the static case). A model is termed classical if in the golden rule state aggregate assets are negative (or debt positive) and Samuelson (following [4]) in the opposite case. It is conjectured that the golden rule program is globally stable in the classical case and the balanced program is stable in the Samuelson case. This is established for the special case n = 2.     

Mixing the carrots with the sticks: third party punishment and reward

While the opportunity to punish selfish and reward generous behavior coexist in many instances in daily life, in most laboratory studies, the demand for punishment and reward are studied separately from one another. This paper presents the results from an experiment measuring the demand for reward and punishment by ‘unaffected’ third parties, separately and jointly. We find that the demand for costly punishment is substantially lower when individuals are also given the ability to reward. Similarly, the demand for costly reward is lower when individuals can also punish. The evidence indicates the reason for this is that costly punishment and reward are not only used to alter the material payoff of others as assumed by recent economic models, but also as a signal of disapproval and approval of others’ actions, respectively. When the opportunity exists, subjects often choose to withhold reward as a form of costless punishment, and to withhold punishment as a form of costless reward. We conclude that restricting the available options to punishing (rewarding) only, may lead to an increase in the demand for costly punishment (reward).     

The expected probability of Condorcet's paradox

Let P(n,p) be the probability that there is a Condorcet winner on three alternatives for n (odd) voters. The vector p defines the probability that a randomly selected voter will have any of the six linear rankings on three alternatives as his or her preference ranking. It is shown that if all p vectors are equally likely, the expected value of P(n,p) is given by 15(n+3)²/[16(n+2)(n+4)].     

Extension of Oi's price instability theorem

Oi's theorem that product price variability raises the average profit of a single-product perfectly competitive firm is generalized in this paper to cover the case of an n-commodity firm. Under similar conditions to those mentioned by Oi for the single-product case, commodity (factor or product) price instability raises the average profit of an n-commodity perfectly competitive firm.     

A progress report on Kelly's majority conjectures

LetC(m, n) be the proportion of n-voter profiles on m alternatives that have a majority winner. Jerry Kelly conjectured that C(m, n) > C(m + 1, n) for m ? 3 and n = 3 and n ? 5, and C(m, n) > C(m, n + 2) for m ? 3 and n ? 3. We prove these for special cases.     

Dynamic decision trees for building resilience into future eco-cities

Intensifying global urbanization and environmental changes bring about the imperative of sustainable urban development and decisions upon inescapable pressures and risks, but knowledge integration between disciplines is a limiting contextual challenge. This paper proposes a reformulation, in terms of urban risk management, of an earlier developed ontological scenario generation method. The procedure consists of several steps: (i) identification-and-prioritization of main pressures, (ii) paired discussion of pressures using four-cell matrices, (iii) re-visit of the pressures' priority order, (iv) articulation of short-listed pressures as decision-making questions, and (v) generation of scenarios via “yes/no” responses to each question, in their order of priority. In this article, the method feeds upon the general context described in recent multi-disciplinary urban studies and public strategic plans in the city of Iasi (Romania), to propose a formal procedure for enabling the acceleration of productive decision making towards city sustainability. Answering three top priority questions, namely “Implement a business-friendly and efficient governance system?”, “Develop a resource management system?”, and “Carry out a human capital accelerator strategy?” results in a 4-scenario set: Receding City, Wanting City, Promising City, Inspiring City. The scenarios are discussed in terms of systemic risks at the end of post-communist transition and beginning of the socio-economic convergence with Western Europe.     

The information matrix test: Simplified calculation via a score test interpretation

In Chesher (1982) I show that the Information Matrix test introduced by White (1982) is a score test for parameter constancy. In this letter I show that this result leads to a simple computational procedure for calculating the Information Matrix test. The procedure involves computing, for a sample of n observations, n times the R² from the least squares regression of a column of ones on a matrix whose elements are functions of 1st and 2nd derivatives of the log density function.     

The network of weighted majority rules and its geometric realizations

In a previous work the first author considered the network G(n,p) of weighted majority rules (WMR) for n decision makers whose competencies are given by their probabilities p=(p₁,…,p_n) of making a correct decision. On this paper we consider chains of decision profiles, which must occur in G(n,p) in a fixed order, and show that they can be mapped onto straight lines in a low-dimensional geometric realization. The minimal number of directions which must used to separate all edges is given as the chromatic number of a certain incidence graph. We also define degenerate networks in which several nodes coalesce.     

Bargaining one-dimensional social choices

We analyze bargaining over the one-dimension characteristic of a public good among n impatient players when decisions require q favorable votes, q?2. Stationary subgame perfect equilibrium strategies are characterized for all games with deterministic protocol. We provide a monotonicity condition (satisfied by all single-peak, strictly quasi-concave and concave utilities) that assures uniqueness for every q whenever player's utilities are symmetric around the peak. Without symmetry, the monotonicity condition assures uniqueness for qualified majorities, q>n/2, provided that agents are sufficiently patient and utilities satisfy an additional regularity condition. Asymptotic uniqueness is assured for qualified majorities by imposing only the monotonicity condition.     

On the investment implications of bankruptcy laws

Axiomatic analysis of bankruptcy problems reveals three major principles: (i) proportionality (PRO), (ii) equal awards (EA), and (iii) equal losses (EL). However, most real life bankruptcy procedures implement only the proportionality principle. We construct a noncooperative investment game to explore whether the explanation lies in the alternative implications of these principles on investment behavior. Our results are as follows (i) EL always induces higher total investment than PRO which in turn induces higher total investment than EA; (ii) PRO always induces higher egalitarian social welfare than both EA and EL in interior equilibria; (iii) PRO induces higher utilitarian social welfare than EL in interior equilibria but its relation to EA depends on the parameter values (however, a numerical analysis shows that on a large part of the parameter space, PRO induces higher utilitarian social welfare than EA).     

Non-parametric test of time consistency: Present bias and future bias

This paper reports the elicited time preference of human subjects in a laboratory setting. The model allows for non-linear utility functions, non-separability between delay and reward, and time inconsistency including future bias in addition to present bias. In particular, the experiment (1) runs a non-parametric test of time consistency and (2) estimates the form of time discount function independently of instantaneous utility functions, and then (3) the result suggests that many subjects exhibiting future bias, indicating an inverse S-curve time discount function.     

Rates of information aggregation in common value auctions

We study the rates at which transaction prices aggregate information in common value auctions under the different information structures in Wilson (Rev. Econ. Stud. 44 (1977) 511) and Pesendorfer and Swinkels (Econometrica 65 (1997) 1247). We consider uniform-price auctions in which k identical objects of unknown value are auctioned to n bidders, where both n and k are allowed to diverge to infinity, and k/n converges to a number in [0,1). The Wilson assumptions lead to information aggregation at a rate proportional to , but the price aggregates information at a rate proportional to in the PS setting. We also consider English auctions, and investigate whether the extra information revealed in equilibrium improves convergence rates in these auctions.     

Tax competition,tax exporting and higher-government choice of tax instruments for local governments

This paper presents a theoretical model with tax exporting due to external ownership of a fraction θ of the land in each local jurisdiction. There are n local jurisdictions in a metropolitan area (n≥1) and many metropolitan areas in a world economy. The paper examines the usage of business property taxes and source-based wage taxes by local jurisdictions, first in the presence of and then in the absence of residence-based lump-sum taxes, and how this depends on θ and n. The paper then examines the choice of a world, national or state government as to whether to allow local (metropolitan or sub-metropolitan) governments to use business property taxes, wage taxes or both, assuming that the local governments choose the actual tax rates.     

A proposed convention for measuring the state of the art of products or processes

During 1980, The Futures Group performed a study under contract to the National Science Foundation to devise a convention for describing—in quantitative terms—technological state of the art of essential any technology. In designing this convention we hope that different analysts, working independently, would be able to arrive at a similar conclusion about the state of the art of a technology under study. With such a measure at hand, it would be possible, for example, to evaluate the effectiveness of investment in R&D by evaluating the improvement in the technological state of the art of a given technology, per unit investment.The form of the equation chosen for the state-of-the-art convention was SOA = K₁(P₁/P'₁ + K₂(P₂/P'₂) ? K_n(P_n/P'_n) where SOA = state of the art, K_n = the relative weight associated with each parameter describing the technology, P_n = the value of the particular parameter useful in describing the state of the art, and P'_n = a reference value of the parameter. Various approaches to the selection of the parameters and their weights were described. Of particular interest is a statistical approach which assumes that the state of the art, over time, is an S-shaped curve. In this instance it is possible to compute the value of the weights through an iterative numerical technique.The convention was applied to two technologies: computers and antibiotics, and state-of-the-art measures were developed for each. In the case of antibiotics, selected organism/antibiotic pairs were analyzed to identify the state of the art of a particular antibiotic as applied to the control of a particular microorganism, over time.     

Farsightedly stable networks

A set of networks G is pairwise farsightedly stable (i) if all possible farsighted pairwise deviations from any network g∈ G to a network outside G are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsighted improving path from any network outside the set leading to some network in the set, and (iii) if there is no proper subset of G satisfying conditions (i) and (ii). A non-empty pairwise farsightedly stable set always exists. We provide a full characterization of unique pairwise farsightedly stable sets of networks. Contrary to other pairwise concepts, pairwise farsighted stability yields a Pareto dominant network, if it exists, as the unique outcome. Finally, we study the relationship between pairwise farsighted stability and other concepts such as the largest pairwise consistent set and the von Neumann–Morgenstern pairwise farsightedly stable set.     

Characterization of the private alternatives domains admitting arrow social welfare functions

An n-person social choice problem is considered in which the alternatives are n dimensional vectors with the ith component of such a vector being the part of the alternative effecting individual i alone. Assuming that individuals are selfish (i is indifferent between any two alternatives that have the same ith component) we characterize all the families of permissible individual preferences that admit nondictatorial Arrow-type social welfare functions. We also show that the existence of such a function for a given family of preferences is independent of n provided that is greater than one.     

A note on the underestimation and overestimation in stochastic input-output models

Here we show that (i) the Leontief inverse (I – A)^-1 is underestimated when the elements of A, the fixed coefficient input–output matrix, are biproportionally stochastic, and (ii) the output vector in a non-linear input–output system is overestimated when the final demand vector is stochastic.     

Development of the extended linear expenditure system from simple saving assumptions

The extended linear expenditure system (ELES) can be developed as an atemporal maximization of a Stone-Geary utility function wherein saving is treated as a good in itself. The key to this development is the a priori specification of the ‘subsistence quantity’ of saving, γ_{n + 1}, to be zero. Thus, the intertemporal maximization approach to the ELES is equivalent to specifying a Klein-Rubin saving function with γ_{n + 1} = 0 for a linear expenditure system (LES) based on permanent income rather than total expenditure. Any income concept - current, normal, or permanent, for example - is acceptable for the ELES developed from the atemporal maximization.     

Balance sheet identity and Walras' Law

The balance sheet identity is interpreted to imply that if n ? 1 of n assets are in stock equilibrium, so is the remaining asset. Under the notion of the end-of-period equilibrium, the following are shown. (1) This interpretation leads to the contradiction that the system does not allow enough independent equilibrium relations to determine uniquely the equilibrium values of its endogenous variables. (2) The balance sheet identity is equivalent to Walras' Law in flow form. Thus, Foley's methodological precept is verified; transforming a period model into its continuous time analogue does not lead to different outcomes from period analysis.