Game Theory and its applications

to social sciences

T.Parthasarathy

Department of Mathematics/ Statistics,

University of Hyderabad, Hyderabad 500044

E.mail:  pacha14@yahoo.com

Abstract

In this talk we will briefly outline the origin of the subject and mention the significance of Game Theory in relation to social sciences. We will also mention some of the recent contributions and indicate the active areas of research in Game

Theory.

 

Assignment Games With Stable Core

T.E.S. Raghavan, University of Illinois at Chicago

T. Solymosi, Budapest Economics University, Hungary

 

Abstract

We prove that the core of an assignment game is stable (i.e., it is the unique von Neumann – Morgenstern solution) if and only if there is a matching between the two types of players such that the corresponding entries in the underlying matrix are all row and column maximums.  We identify other easily verifiable matrix properties and show their equivalence to various known sufficient conditions for core-stability.  By these matrix characterizations we found  that on the class of assignment games, largeness of the core, extendibility and exactness of the game are all equivalent conditions, and strictly imply the stability of the core.  In turn, convexity and subconvexity are equivalent, and strictly imply all aforementioned conditions.

 

 

 

 

 

 

 

Study on Improvement of Availability and Utilization of Tippers

Prasun Das

SQC & OR Unit

Indian Statistical Institute

27B, Camac Street

Kolkata-16, India

e-mail : dasprasun@hotmail.com

 

Abstract

Availability of the tippers is vital for achieving high productivity in any quarry. Substantial improvement of availability and utilisation of tippers under the existing infrastructure of the system was of primary concern to a plant management.

Performance  of  all  the tippers was evaluated  through Mean Time-to-Failure and Mean Down Time including the overall system performance. Based on Weibull(b,c) and Exponential(l) distributions, the reliability of all the tippers (component reliability) along with the overall system reliability with respect to 10-out-of-17 structure were computed. Next, tippers were clustered, using k-means clustering algorithm, and the group reliabilities were obtained which led to different options for improving the overall system’s reliability.

The minimum number of repairmen required to keep the desired number of tippers running with a certain probability was determined, through simulation technique, using the classical Repairmen model. To facilitate the maintenance strategy for the repairmen, self-inducing failure modes were identified using interrelationship matrix.

Implementation of suitable preventive maintenance activities along with overhauling, training, ordering strategy of spare parts and maintenance crew restructuring resulted in an increase in average utilisation of tippers from 66.8% to the level of 75%, whereas the system availability has improved to 85.75% from the earlier level of 78.34%.

 

Maximizing Utilization of Furnace in a Foundry Satisfying Multiple Objectives

Susanta Kumar Gauri

SQC & OR Unit

Indian Statistical Institute

27B, Camac Street, Kolkata-700016, India

e-mail:susantagauri@hotmail.com

 

Abstract

In a foundry producing ferrous castings, the typical operations needed for production of castings include

a)      preparation of molds,

b)      preparation of green sand and packing of the molds with green sand inside mold boxes

c)      preparation of molten metal (i.e. melt),

d)      pouring the melt into the mold boxes (i.e. packed molds), and

e)      separating the castings from the molds after necessary cooling.

The time span from the loading of ingredients into the furnace to the completion of pouring of the melt is known as heat length (in short, heat). In a single heat different types of casting are produced when the required composition for all the types are similar. The fixing of different types to be cast and their quantities to be produced in a heat is known as product-mix. The quantity that should be charged in furnace depends on this product-mix considered for a heat. On the other hand, once the pouring operation begins it has to be completed without a break. Therefore the starting of the pouring operation is delayed until all the molds of the product-mix considered are not ready after packing; otherwise leftover quantity of melt in the furnace becomes high. The maximization of utilization of furnace implies that in each heat the furnace is charged to its capacity and leftover quantity of melt after pouring is complete is as little as possible, and number of heats in a day be as many as possible. In order to maximize number of heats in a day there should not be shortage in packing resources. However, deployment of too many resources for packing incurs unnecessary cost. Leftover quantity of melt in furnace, packing cost as well as failure of delivery commitments all depend on the product-mix considered. Therefore, it was essentially a problem of determination of optimal product-mix under multiple conflicting objectives. The priority based linear goal programming was used to formulate the model. The optimal product-mix as well as the amount of extra resources needed for packing molds of the optimal product-mix was determined.

 

Operations Research in planning and provision of HIV/AIDS related

services-A review

B.Sudha

Institute of  Community Medicine,

Madras Medical College & Govt. Gen. Hospital,

Chennai-600 003.

 

Abstract

The HIV/AIDS epidemic is one of the biggest global challenges in the history of public health. With millions already infected, the potential health and socioeconomic impact of AIDS is cause for serious concern. There is a compelling need to chalk out well-designed, effective strategies that will halt the spread and reduce the impact of the epidemic.

Research in the field of HIV/AIDS is predominantly in two dimensions- a clinical focus, aimed at better medical understanding of the disease process and an epidemiological focus, which looks at modeling transmission and hence forecasting. Another important dimension of AIDS research that by comparison, has received little attention is the ‘services planning’ dimension. Policy makers and intervention designers need to focus on  the optimal mix of actions needed. Their design and funding levels have been driven more by advocacy of the programme beneficiaries/managers and politics than by reasoned analysis. This paper explores the emerging areas of operations research in the field of HIV/AIDS with a view to improve decision making for planning, resource allocation and public health policy.

 

Linking of Rivers

R,sunder babu        K. alagar,

Dept. of commerce, yadava college,

madurai.625 014

 

Abstract

Linking of rivers is the need of the hour for India. It results in a major change in the

economical, sociological, human and envirnnonmental aspects. This paper is projecting a CPM/ PERT model for the linking of rivers by taking in to account the

activities such as resource generation, budget allocation, land acquisition, water sharing agreement, dam construction.

 

Application of Game Theory in the Pricing of Mobile Services

Vigeendharan S          Sampath Kumar J      Athilakshme N

Anna university

Chennai

Abstract

The issue of strategic pricing on the part of the regulator and service provider of telecom services is dealt in this paper. The technology has made it possible to provide

internet based services in a mobile. Since the internet and mobile services are coupled up, the regulator has to consider new services provided, to device a strategy that will uphold the competition in the industry. With many players in Indian telecom sector ,the scenario is a classic example of N-person mixed strategy game The uniqueness of the telecom industry is that the presence of many players has given rise to a coalition which makes both co-operative and non Co-operative games possible. We have considered coalitions in which there is no Transferable utility, which allows players to make side payment. The core of each coalition is developed taking into consideration the strategic equivalent nature of services provided. The different number of players that a regulator can allow is also discussed based on the market potential of a service .The telecom service providers play a mixed strategic

game of pricing based on the services they offer and the cost of providing the service. In the end the nucleolus of service providers is arrived at  based on the demand of each service.

Key Words: N person mixed strategy game, Strategic Equivalence, Nash

Equilibria and General Equilibria   

 

Refinement of solutions to the linear complementarity problem and applications

S. R. Mohan

SQC & OR Unit

Indian Statistical Institute

7, S. J. S Sansanwal Marg

New Delhi 110 016

 

Abstract

 This talk is based on a joint work with Talman and Neogy. The concept of refinement of solutions is well known in non-cooperative game theory and has been studied by Selten and Van Damme.  This notion is extended to the solutions of a linear complementarity problem in this presentation, and its application to mathematical programming problems is studied.

 

A note on linear complementarity problems and multiple objective programming

S.R. Mohan1 Contact Information, S.K. Neogy1 and A.K. Das2

(1)

Indian Statistical Institute, New Delhi, 110016

 

(2)

Indian Statistical Institute, Calcutta, 700 035

Published online in Mathematical Programming: 30 September 2003

Abstract

Kostreva and Wiecek [3] introduced a problem called LCP-related weighted problem in connection with a multiple objective programming problem, and suggested that a given linear complementarity problem (LCP) can be solved by solving the LCP-related weighted problem associated with it. In this note we provide several clarifications of the claims made in [3]. Finally, we feel that solving any LCP by the approach given in [3] may not be as useful as it is claimed.

Keywords  linear complementarity problem - lemke''s algorithm - LCP-related weighted problem - multiple objective programming problem

Mathematics Subject Classification (2000):90C33

 

 

 

 

 

Affine Quasimonotone and Pseudomonotone  mappings on the nonnegative orthant and the linear complementarity problem

S. K. Neogy

Indian Statistical Institute

7, S. J. Sansanwal Marg

NewDelhi-110 016

E. mail: skn@isid.ac.in  

Abstract

In this talk, we consider  linear complementarity problem involving quasimontone and pseudomonotone affine maps on  the nonnegative orthant .We study and characterize pseudomonotone and  quasimontone matrices in terms of positive subdefinite matrices. Finally we show that if a matrix A is sum of a Non Positive semidefinite pseudomonotone  matrix and a copositive matrix then Lemke’s algorithm solve LCP(q,A). This talk is based on a joint work with Mohan and A. K. Das.

 

Patent Licensing in a Leadership Structure

Tarun Kabiraj*

Economic Research Unit

Indian Statistical Institute,

203 B. T. Road, Kolkata – 700108, India.

E-mail: tarunkabiraj@hotmail.com

Abstract

This paper studies the question of an optimal licensing contract in a leadership structure when the patent holder is a non-producer, and has three alternative licensing strategies, viz., fixed fee, royalty and auction. Assuming once-for-all licensing contracts we show that royalty dominates other modes when the innovation is small. For larger innovations while fee dominates royalty, auction is the equilibrium decision. In our analysis the identity of the licensee, whether a leader or a follower, is important. We also discuss the problem when there is a threat of offering a second licensing contract.

Key words: Leadership structure, process innovation, fee licensing, royalty licensing, auctioning.

JEL classifications: D45, L13.

 


*I would like to thank an anonymous referee of this journal for valuable comments and suggestions. Discussion with Uday Bhanu Sinha was also rewarding. However, I shall be held responsible for any remaining errors.

 

Trade Liberalization, Quality competition and Optimal product

 Range  of an MNC

Rajat Acharyya

Department of Economics

Jadavpur University

Kolkata:  700 032

E.mail:  racharaya@cal2.vsnl.net.in

 

Abstract

 

Often foreign MNCs entering an erstwhile-protected LDC-market are observed to cater to only the upper segments instead of to all segments of the market. Indian automobile market is one such example.

An obvious explanation of such an entry pattern is that though the foreign entrants may have lower marginal cost of producing higher quality varieties, they have absolute cost disadvantage in producing lower quality varieties, which arises due to initial substantial costs involved in setting up of production units and distribution network in the LDC-market. An alternative argument, often subscribed by managers of the MNCs, is that upper segment of the market offers a higher premium over costs because consumers there are willing to pay much more for a higher-quality product than consumers in the lower segments. Offering a product range that targets several segments of the market, limits the firm’s ability to extract greater surplus from such “high-type” consumers and thus is not a optimal strategy unless the size of these consumers is small relative to consumers in the lower segments. In fact, demand-pattern is the key element in deciding about the product range when the foreign MNCs have absolute cost advantage over the local rival(s) in producing all feasible quality levels.

 

The purpose of this paper is to formalize this argument and derive precise conditions for the decision of an entrant to offer only the high-quality product targeted to high-type consumers instead of offering a wide range of products targeted to all types of consumers. In a simple model of a vertically differentiated market with only two types of consumers, where a domestic incumbent correctly anticipating a foreign entrant’s optimal menu(s) selects price-quality menus before entry actually takes place, we examine choice of product range by the foreign entrant when it has only a relative cost advantage in producing higher-quality varieties and when it has absolute cost advantage in producing all the varieties.

 

Two other results derived in the paper deserve attention. First, the threat of competition from the foreign entrant, regardless of its technological superiority, forces the domestic incumbent to enhance the pre-liberalization product quality offered to the low-type consumers. This lends theoretical support to the popular perception that trade liberalization and foreign competition has a favourable impact on domestic product qualities. Second, welfare implications of trade liberalization depend on the nature of technological superiority of the foreign entrant.

 

Joint Venture, Independent Subsidiary and Foreign

Ownership - A Welfare Analysis

Tarun Kabiraj                                      Sugata Marjit

                     Economic Research Unit            Centre for Studies in Social Sciences

                  Indian Statistical Institute               R-1, Baishnabghata Patuli Township

                   203 B. T. Road, Kolkata-108                                Kolkata

        E-mail: tarunkabiraj@hotmail.com                  E.mail: smarjit@hotmail.com

 

Abstract

 This paper provides a welfare analysis of policies that allow for fully owned subsidiary of a foreign firm in the presence of an existing joint venture. We relate our work to a current and controversial regulatory issue in India. Is it reasonable to compel the foreign firm to obtain a No Objection Certificate (NOC) from the existing partner or to allow it to go for a new venture independent of the concern of the existing partner? We develop a Cournot model with side payment, where technological differences between the firms matter. The trade off seems to lie in the degree of existing ownership, the rise in consumers’ surplus and the quality of technology available for the subsidiary. We obtain several results. One interesting aspect seems to be that a policy allowing the subsidiary to be opened could be optimal when the existing partner is reluctant to issue an NOC and the same policy may not be optimal when NOC is issued without much of a problem. Since policymaker's strategy depends on Cournot outcomes as well as incentives of the participating firms, it seems to be an interesting problem to work with.

 

On Patent Licensing in Spatial Competition

Sougata Poddar      Uday Bhanu Sinha

      National University of Singapore        Indian Statistical Institute, Calcutta

 

Abstract

We consider the issue of patent licensing in a linear city framework where firms are located at the end points of the city and compete in price. We consider three types of licensing arrangements, namely, auction, fixed fee, royalty; and focus on the optimal licensing strategy of an outsider patentee as well as an insider patentee. Contrary to the findings in the existing literature, first we show offering royalty is the best for the patentee when the patentee is an outsider for both drastic and non-drastic innovation. For insider patentee, offering no-license is the best when the innovation is drastic, while royalty is optimal when the innovation is non-drastic. We find incentive for innovation is higher for an outsider patentee compared to an insider patentee. We also show that overall increase in welfare due to an innovation is independent of the fact that the patentee is outsider or insider in each of the drastic and non-drastic case.