Jyotirmoy Sarkar

Spatial Cournot competition and agglomeration in a model of location choice

Abstract Consider a two-stage non-cooperative Cournot game with location choice involving n ⩾ 2 competing firms. There are spatially contiguous markets along the interval [0,1] with relative size of the markets described by a continuous density function φ(x). The demand function for each individual consumer is the same in each market. Each firm first selects the location of its facility and then selects the quantities to supply to the markets, so as to maximize its profit. Earlier works on Cournot competition in spatial models have shown, assuming that the consumers are distributed uniformly over the markets, that firms typically tend toward central agglomeration. This paper extends the previous work by establishing the robustness of the agglomeration equilibrium to a broad class of density functions. Derived here are conditions under which: (i) agglomeration of all n firms is an equilibrium, (ii) agglomeration of duopolists is the only equilibrium, and (iii) duopolists exhibit a dispersed equilibrium. Examples of partial agglomeration are also constructed.

Spatial competition among multi-store firms

Abstract The paper analyzes spatial Cournot competition among multi-store firms. It demonstrates that the complex problem of determining equilibrium store locations for competing multi-store firms can be approximated by a simple one, in which each firm behaves as a multi-store monopolist in choosing its store locations. A firm’s equilibrium store locations often coincide with its monopoly locations, and in general, converge to its monopoly locations as the demand grows larger. When the firms have an equal number of stores, the stores belonging to competing firms agglomerate at discrete points that coincide with each firm’s monopoly store locations.

Availability of a periodically inspected system under perfect repair

We study the availability of a system that is maintained under periodic inspection and a perfect repair policy with constant repair time. We consider two models. One, Model A that treats an unfailed system to be as good as new upon inspection, and makes perfect repair of a failed system with immediate restoration. Two, Model B that does not intervene on a system found unfailed at inspection times and makes perfect repair of a failed system with restoration taking place at the next scheduled inspection following repair. For each model, we express the system availability function as a linear combination of the survival function and its shift(s), and, thereby, obtain the limiting average availability. We illustrate the results when the system has exponential or gamma life distribution. Graphs of the system availability function, and numerical tables showing the limiting average availability and the periodicity of inspections necessary to achieve a specified limiting average availability are also presented.

Availability of a system maintained through several imperfect repairs before a replacement or a perfect repair

Employing the Fourier transformation technique, we find the availability of a system maintained through several imperfect repairs before a replacement or a perfect repair is allowed. We obtain exact expressions for the availability when both lifetime and repair time distributions are exponential (with possibly different parameters). Comparison is made with the system availability under the perfect repair policy.

Availability of a periodically inspected system, maintained under an imperfect-repair policy

A periodically inspected system is maintained through a fixed number of imperfect-repairs before being replaced or perfectly repaired. The lifetime distribution of the system in its new and imperfectly repaired states is arbitrary. The times required for imperfect repairs and for perfect repair or replacement are random. The repaired system is restored to operation at the next scheduled inspection time. The system availability function is expressed as the weighted average of the survival functions and their shifts, and gives the limiting average availability.

Availability of a system with gamma life and exponential repair time under a perfect repair policy

Employing Fourier transform technique we determine the availability of a maintained system under continuous monitoring and with perfect repair policy. We obtain closed-form expressions for the availability when the system has gamma life distribution and the repair time is exponential.

Location Equilibrium for Cournot Oligopoly in Spatially Separated Markets

Consider a two-stage non-cooperative Cournot game with location choice involving n≥ 2 firms each with several facilities. There are m≥ 2 spatially separated markets constituting the vertices of a network. Each firm first selects the locations of their facilities and then selects the quantities to supply to the markets to maximize its profit. There exists a Nash equilibrium in the quantities offered by each firm at the markets. Furthermore, when the demand in each market is sufficiently large, each firm chooses to locate its facilities only at vertices. With linear demand in each market, there exists a Nash location equilibrium.

A Stackelberg Oligopoly with Nonidentical Firms

This paper extends the Stackelberg model to include any number of nonidentical firms and demonstrates significant counterintuitive results. For example, entry of an additional firm may increase the quantities and/or profits of some existing firms; it may also increase the total industry profit. Copyright 2001 by Blackwell Publishing Ltd and the Board of Trustees of the Bulletin of Economic Research

Availability of a periodically inspected system supported by a spare unit, under perfect repair or perfect upgrade

The exact availability and the limiting average availability of a periodically inspected system, supported by a spare and maintained with perfect repairs or upgrades, are obtained for arbitrary life-, repair- and upgrade-time distributions. Illustrative examples, graphs and table are presented.

A standby system with two repair persons under arbitrary life- and repair times

A continuously monitored one-unit standby system is perfectly repaired either by an in-house regular repairer within a predetermined patience time, or else by a visiting expert repairer, who repairs all failed units. For arbitrary life- and repair times, we present a procedure to find the limiting proportions of time the system stays in each state using extended semi-Markov processes, whence we can find other limiting characteristics.