Binary effectivity rules

A social choice rule (SCR) is a collection of social choice correspondences, one for each agenda. An effectivity rule is a collection of effectivity functions, one for each agenda. We prove that every monotonic and superadditive effectivity rule is the effectivity rule of some SCR. A SCR is binary if it is rationalized by an acyclic binary relation. The foregoing result motivates our definition of a binary effectivity rule as the effectivity rule of some binary SCR. A binary SCR is regular if it satisfies unanimity, monotonicity, and independence of infeasible alternatives. A binary effectivity rule is regular if it is the effectivity rule of some regular binary SCR. We characterize completely the family of regular binary effectivity rules. Quite surprisingly, intrinsically defined von Neumann–Morgenstern solutions play an important role in this characterization.     

On the continuity of representations of effectivity functions

An effectivity function assigns to each coalition of individuals in a society a family of subsets of alternatives such that the coalition can force the outcome of society’s choice to be a member of each of the subsets separately. A representation of an effectivity function is a game form with the same power structure as that specified by the effectivity function. In the present paper we investigate the continuity properties of the outcome functions of such representation. It is shown that while it is not in general possible to find continuous representations, there are important subfamilies of effectivity functions for which continuous representations exist. Moreover, it is found that in the study of continuous representations one may practically restrict attention to effectivity functions on the Cantor set. Here it is found that general effectivity functions have representations with lower or upper semicontinuous outcome function.     

The influence of relational experience and contractual governance on the negotiation strategy in buyer–supplier disputes

This paper theoretically refines and empirically extends the debate on the type of interplay between relational experience and contractual governance in an under-researched area: supply chain disputes. We define relational experience as either cooperative or competitive; distinguish between control and coordination functions of contractual governance; and assess their interplay on the negotiation strategy used in disputes. Using a unique data set of buyer–supplier disputes, we find, in particular that increasing contractual control governance weakens the positive effect of cooperative relational experience on cooperative negotiation strategy. However, increasing contractual control governance for a buyer–supplier dyad with competitive relational experience will increase cooperative negotiation strategy. Contractual coordination governance reinforces the positive effect of cooperative relational experience. Through this study, we reach a better understanding of how and when contractual and relational governance dimensions interact; rather than whether they act as substitutes or complements as has been studied in prior research. We discuss the implications of these findings for the field of supply chain management.     

An approximation to the finite sample distribution of Zellner's seemingly unrelated regression estimator

A multiple equation model of the seemingly unrelated regressions type is considered. We derive an Edgeworth expansion up to 0(T^-1), where T is the sample size, of the finite sampls distribution function of the seemingly unrelated regression estimator of the parameters in thie model. We examine the two-equation case where our results can be related to exact theory in the special case of orthogonal exogenous variables and we take as a particular numerical example Zellner's original application to micro-investment functions.     

An evaluation framework for developing green infrastructure by using a new hybrid multiple attribute decision-making model for promoting environmental sustainability

With the expansion of urbanization caused by the growth of population and industrial activities, the urban/city and suburban areas are facing a variety of environmental threats. Although more research and urban policy has advocated and practiced the development of green infrastructure (GI) to support urban sustainable environment, the evaluation framework for the development of GI for promoting environmental sustainability is still insufficient. Moreover, the Analytic Hierarchy Process (AHP) commonly applied in published literature, makes an unrealistic assumption of independent relationships among dimensions/criteria in decision making for satisfying the real-world problem. Therefore, the purpose of this study is to construct the evaluation framework, including four dimensions and related ten criteria, using a new hybrid-modified multiple attribute decision-making (MADM) model for developing and improving the GI for promoting environmental sustainability. This MADM model is combined with three different methodologies of MADM, including the Decision-Making Trial and Evaluation Laboratory (DEMATEL) for constructing the influential network relation map (INRM) to explore the complex influential inter-relationships and DEMATEL based on Analytic Network Process (DANP) for determining the influential weights with the VIse Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) for evaluating and presenting improvement strategies for six different GIs. The empirical study indicates that DEMATEL and DANP Results suggest that decision-makers should pay more attention to the improvement of Design (D₄) and Materials (D₂) in terms of dimensions when utilizing the GI to promote environmental sustainability. Because these dimensions are enhanced, Species (D₁) and Energy (D₃) will be improved in synchronization. From the perspective of criteria, five are key core criteria and need to be focused on first: increasing the green coverage rate (B₉), utilizing sustainable materials (B₄), using ecological engineering (B₈), shaping species biodiversity (B₁), and reducing energy consumption (B₅). Modified VIKOR reveals that “grass swales” are a comparatively better choice among six GIs for promoting environmental sustainability toward achieving the aspiration level. Therefore, this MADM model is beneficial to provide a more convincing assessment framework and improvement strategies for the development of GI for promoting environmental sustainability. As a result, these modified MADM models can be shown more conveniently and reasonably than traditional methods such as traditional AHP or ANP method.     

A note on compact differentiability and theδ-method

Letη _n ,n ∈ ?, be arbitrary functions defined on a probability space (ω,A,P) with values in a normed vector spaceB ₁ ,μ ∈ B ₁ andξ ₀ a separable random element inB ₁ such thatξ _n :=√n(η _n ?μ) converges weakly toξ ₀ in the sense of Hoffmann-Jørgensen. Then with (B ₂, ∥·∥₂) being another normed vector space andφ:B ₁→B ₂ compactly differentiable atμ with derivateD _μ, the random variable $\parallel \sqrt n (\phi (n_n ) - \phi (\mu )) - D_\mu (\sqrt n (n_n - \mu ))\parallel 2*$ converges to 0P-stochastically where “*” denotes the measurable cover. We show that the classicalδ — method extends to the non-measurable case where in the proof we shall not make use of any representation theorems but only of a slight refinement of the usual characterisation of compact differentiability, due to the fact that we will not assume {ξ _n :n ∈ ?} being tight.     

The stability of the demand for fossil fuels by electric utilities

The view that the regional demand for fossil fuels by electric utilities in the United States is characterized by stable relationships is subjected to an objective statistical test. The test utilizes a statistic which equals the ratio of the sum of squared residuals of one period prediction from the k + 1 period to the rth period to the sum of squared residuals of one period prediction from the k + 1 to the Tth period, where k is the number of estimated coefficients in the model and T is the sample size. The results suggest for the period 1973 through 1978, that the fossil fuel demand functions in Region II and Region VIII and the coal demand function in Region X became unstable around 1977. For the other regions, the results indicate no appreciable (statistically significant) change in the relative importance of the underlying determinants of the demand for fossil fuels.     

Competitive prizes: when less scrutiny induces more effort

We consider a principal who is keen to induce his agents to work at their maximal effort levels. To this end, he samples n days at random out of the T days on which they work, and awards a prize of B dollars to the most productive agent. The principal’s policy (B, n) induces a strategic game Γ(B, n) between the agents. We show that to implement maximal effort levels weakly (or, strongly) as a strategic equilibrium (or, as dominant strategies) in Γ(B, n), at the least cost B to himself, the principal must choose a small sample size n. Thus less scrutiny by the principal induces more effort from the agents.The need for reduced scrutiny becomes more pronounced when agents have information of the history of past plays in the game. There is an inverse relation between information and optimal sample size. As agents acquire more information (about each other), the principal, so to speak, must “undo” this by reducing his information (about them) and choosing the sample size n even smaller.     

A coalitional game-theoretic model of stable government forms with umpires

In this paper a government form is modeled as an effectivity function scheme (EFS) i.e. a parameterized family of effectivity functions having admissible weight-profiles of assemblies as the relevant parameters. Working in a 2-jurisdiction outcome space we show that the existence of umpires is consistent with strong core-stability of both neo-parliamentary and semi-presidential government forms provided that the majority formation rule is collegial, namely there is one electorally fixed minimal majority coalition.      

Third-order optimum properties of estimator-sequences

SequencesT ⁽ⁿ⁾ ,n∈N, are considered, whereT ⁽ⁿ⁾ estimates a vector parameter ?∈R ^p from an i.i.d. sample of sizen, and such sequences are compared on the basis of their risks ∫L(n ^1/2(T ⁿ (x)?θ))P _θ ⁿ (dx) relative to loss functionsL:R ^p →R. A characterization is given for sequencesT ^*(n) ,n∈N, which generate an essentially complete class in the following sense: For any sequenceT ⁽ⁿ⁾ ,n∈N, there exist functions Φ _n ,n∈N, such that forn→∞ we have $$\begin{gathered} \smallint L (n^{1/2} (T^{*(n)} + n^{ - 1} \Phi _n (T^{*(n)} ) - \theta )) dP_\theta ^n \leqslant \hfill \\ \leqslant \smallint L (n^{1/2} (T^{(n)} - \theta )) dP_\theta ^n + o (n^{ - 1} ), \hfill \\ \end{gathered} $$ for every ? and everyL satisfying certain conditions. If the estimator-sequences are compared by their risks ∫W(T ⁽ⁿ⁾ d P _θ ⁿ ,θ) with respect to loss functionsW:R ^p ×Θ→R then a similar result on asymptotically complete classes is valid. The results are obtained under the assumption thatT ^*(n) ,n∈N, andT ⁽ⁿ⁾ ,n∈N, admit stochastic expansions which are sufficiently regular, that the loss functionsL andW are sufficiently smooth and bounded by polynomials, and that the estimator-sequences have asymptotically bounded moments; the latter condition is not needed for bounded functionsL andW.     

Correcting for truncation bias caused by a latent truncation variable

We discuss estimation of the model Y_i=X_ib_Y+e_Yi, T_i=X_ib_T+ e_Ti, when data on the continuous dependent variable Y and on the independent variables X are observed iff the ‘truncation variable’ T>0 and when T is latent. This case is distinct from both (i) the‘censored sample’ case, in which Y data are available iff T>0, T is latent and X data are available for all observations, and (ii) the ‘observed truncation variable’ case, in which both Y and X are observed iff T>0 and in which the actual value of T is observed whenever T>0. We derive a maximum-likelihood procedure for estimating this model and discuss identification and estimation.     

Some properties of the LIML estimator in a dynamic panel structural equation

We investigate the finite sample and asymptotic properties of the within-groups (WG), the random-effects quasi-maximum likelihood (RQML), the generalized method of moment (GMM) and the limited information maximum likelihood (LIML) estimators for a panel autoregressive structural equation model with random effects when both T (time-dimension) and N (cross-section dimension) are large. When we use the forward-filtering due to Alvarez and Arellano (2003), the WG, the RQML and GMM estimators are significantly biased when both T and N are large while T/N is different from zero. The LIML estimator gives desirable asymptotic properties when T/N converges to a constant.     

Constitutional implementation

We consider the problem of implementing a social choice correspondence H in Nash equilibrium when the constitution of the society is given by an effectivity function E. It is assumed that the effectivity function of , is a sub-correspondence of E. We found necessary and efficient conditions for a game form to implement H (in Nash equilibria), and to satisfy, at the same time, that , the effectivity function of , is a sub-correspondence of (which guarantees that is compatible with E). We also find sufficient conditions for the coincidence of the set of winning coalitions of and , and for . All our results are sharp as is shown by suitable examples. Received: 15 December 2000 / Accepted: 3 September 2001     

A stochastic bargaining process for n-person games

A stochastic bargaining process for a cooperative n-person game is investigated. The bargaining consists of proposing a sequence of utility vectors each of which improves upon (blocks) the foregoing one. In this sequence the proposals are chosen according to a transition probability fulfilling some regularity conditions. It can be proved that almost every sequence converges to an imputation in the core of the game. Further, the probability of ending up in a neighborhood of the core converges quickly to one as the number of proposals goes to infinity.     

Estimation in the first-order moving average model through the finite autoregressive approximation: Some asymptotic results

To estimate α in the model y_t = u_t+αu_t?1, we consider a proposal by Durbin (Biometrika, 1969). It consists in fitting an autoregression of order k to the data, and deriving from there an estimate α^. The probability limit and the variance of the limiting normal distribution of α^ are presented and discussed in detail, when the sample size T → ∞, but k remains fixed. The differences between the resulting values and those corresponding to the maximum likelihood estimator are exponentially decreasing functions of k. Several modifications of the estimator are discussed and found consistent, but asymptotically inefficient.     

Reduced rank regression in cointegrated models

The coefficient matrix of a cointegrated first-order autoregression is estimated by reduced rank regression (RRR), depending on the larger canonical correlations and vectors of the first difference of the observed series and the lagged variables. In a suitable coordinate system the components of the least-squares (LS) estimator associated with the lagged nonstationary variables are of order 1/T, where T is the sample size, and are asymptotically functionals of a Brownian motion process; the components associated with the lagged stationary variables are of the order T^−1/2 and are asymptotically normal. The components of the RRR estimator associated with the stationary part are asymptotically the same as for the LS estimator. Some components of the RRR estimator associated with nonstationary regressors have zero error to order 1/T and the other components have a more concentrated distribution than the corresponding components of the LS estimator.     

Two machine scheduling problem when passing allowed

Bagga [1967] andJohnson [1954] developed algorithms for finding an optimum sequence, whenn jobs require processing on two machines. The criteria chosen by them were minimum waiting time of jobs and minimum elapsed time respectively. All then jobs were assumed to be of the same type i.e., all have to be processed on two machinesA andB in the orderAB. This paper presents a procedure for finding the optimal schedule of the jobs, when the jobs may be of the following types:

1. Jobs which are to be processed on only one of the machines.
2. Jobs which require processing on the two machinesA andB in the orderAB; and
3. Jobs which require processing on the two machinesA andB in the orderBA.

     

Capital procurement of a consumer cooperative: Role of the membership market

Cooperative firms are commonly thought to be financially weak and unable to flourish in the market economy. This paper addresses the idea that a consumer cooperative issues a membership, which represents an ownership share in the cooperative, as a method of procuring equity capital. It then shows that, in theory, consumer cooperatives are not necessarily financially weaker than investor-owned firms in the presence of a membership market. This implies that the consumer cooperative is potentially a promising alternative to the investor-owned firm when the latter type of firm induces serious market failure in the product market.     

Revelations of a gambler

Knowing that a decision maker maximizes expected utility with respect to some (unknown) utility U and some (unknown) probability P, what can one tell about P by observing his decisions? We discuss this revealed preference question primarily in the simple case of a two-element (H and T) state space, and show that the possible revelations of P_T/P_H are precisely those of the form P_T/P_Hε∪^K_k=1 (γ_k,δ_k), for some algebraic numbers γ_k,δ_k.     

On the properties of the hotelling��s T2 control chart with variable sampling intervals

When T ² control chart is used to monitor a process, it is usually assumed that the samples of size n ₀ is taken at constant intervals t ₀ . In this paper, we investigate the T ² control chart for monitoring the process mean vector when the sampling intervals are variable. Recent studies have shown that the variable sampling interval (VSI) scheme helps practitioners detect process shifts more quickly than the classical scheme Fixed Ratio Sampling (FRS). In this paper, it is assumed that the length of time the process remains in control is exponentially distributed.