Free Riding on Hot Wheels

When warehouse clubs started making inroads into its market, Toys R Us responded with a policy designed to limit the clubs\u27 access to certain toys. The FTC successfully challenged the policy, arguing that TRU had coordinated a horizontal agreement amongst the toy manufacturers to eliminate competition from this new class of competitors. TRU defended itself, invoking the free-rider rationale. This the Commission rejected as pretext. TRU\u27s argument was better than the Commission gave it credit for, but it failed to press its best argument. That failure stems in part from the shortcomings of the standard free rider formulation, and in part from the defendant\u27s need to tailor its arguments to ill-fitting doctrinal constraints. TRU attempted to convince the Commission that its actions were unilateral, within the Colgate exception. Perhaps they were, although the Commission found to the contrary. Regardless, the net result was suppression of an efficiency rationale that emphasized the benefits of cooperation by the toy manufacturers. In this paper, I will argue that TRU emphasized the wrong free rider problem. Properly framed, the behavior of TRU and the toy companies can be seen as consistent with the efficiency goals of antitrust policy. That a plausible efficiency argument can be constructed does not mean that the outcome itself was wrong. My narrow focus here is on showing that the standard formulation led to asking the wrong question. Part I provides a brief overview of the market and TRU\u27s behavior. Part II summarizes the defense\u27s rationale and the Commission\u27s rejection of it. Part III provides an alternative explanation. Part IV concludes

(SI10-077) A Novel Collocation Method for Solving Second-order Volterra Integro-differential Equations

In this article, we present an efficient numerical methodology to solve second-order linear Volterra integro-differential equations. Further, the modified Chebyshev collocation method is used at the Gauss-Lobatto collocation points. In that context, some theoretical investigation related to error analysis is suggested through residual function. Numerical examples are also encountered to study the applicability of the present method. In order to get a vivid illustration of the efficiency, we present a comparative survey with three existing collocation methods

On I-Limit Superior and I-Limit Inferior of Sequences in Intuitionistic Fuzzy Normed Spaces

In this article we introduce the notions of I-limit superior and I-limit inferior for sequences in intuitionistic fuzzy normed linear spaces and prove intuitionistic fuzzy analogue of some results of I-limit superior and I-limit inferior for real sequences. The concept of I-limit points and I-cluster points in intuitionistic fuzzy normed linear spaces are introduced and some of their properties have been established

Kronecker factorial designs for multiway elimination of heterogeneity

Efficiency, Kronecker product, orthogonal array, orthogonal factorial structure, projection,

Inverse Eigenvalue Problems for Two Special Acyclic Matrices

In this paper, we study two inverse eigenvalue problems (IEPs) of constructing two special acyclic matrices. The first problem involves the reconstruction of matrices whose graph is a path, from given information on one eigenvector of the required matrix and one eigenvalue of each of its leading principal submatrices. The second problem involves reconstruction of matrices whose graph is a broom, the eigen data being the maximum and minimum eigenvalues of each of the leading principal submatrices of the required matrix. In order to solve the problems, we use the recurrence relations among leading principal minors and the property of simplicity of the extremal eigenvalues of acyclic matrices

Inverse eigenvalue problems for acyclic matrices whose graph is a dense centipede

The reconstruction of a matrix having a pre-defined structure from given spectral data is known as an inverse eigenvalue problem (IEP). In this paper, we consider two IEPs involving the reconstruction of matrices whose graph is a special type of tree called a centipede. We introduce a special type of centipede called dense centipede.We study two IEPs concerning the reconstruction of matrices whose graph is a dense centipede from given partial eigen data. In order to solve these IEPs, a new system of nomenclature of dense centipedes is developed and a new scheme is adopted for labelling the vertices of a dense centipede as per this nomenclature . Using this scheme of labelling, any matrix of a dense centipede can be represented in a special form which we define as a connected arrow matrix. For such a matrix, we derive the recurrence relations among the characteristic polynomials of the leading principal submatrices and use them to solve the above problems. Some numerical results are also provided to illustrate the applicability of the solutions obtained in the paper