Mathematical Programming and Game Theory for Decision Making Volume 1 1st Edition by SK Neogy, RB Bapat, AK Das, Parthasarathy, Sankar Pal ISBN 9789812813220 9812813225

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ISBN 10: 9812813225
ISBN 13: 9789812813220
Author: SK Neogy, RB Bapat, AK Das, Parthasarathy, Sankar Pal

Mathematical Programming and Game Theory for Decision Making Volume 1 1st Edition Table of contents:

1. Mathematical Programming and its Applications in Finance L. C. Thomas

Abstract

1.1 Introduction

1.2 Portfolio Optimization

1.3 Asset-liability Models

1.4 Yield Curves

1.5 Credit Scorecards

Bibliography

2. Anti-stalling Pivot Rule for Linear Programs with Totally Unimodular Coe cient Matrix S. N. Kabad

Abstract

2.1 Introduction

2.2 Pivot Selection Rule

Bibliography

3. A New Practically E cient Interior Point Method for Convex Quadratic Programming K. G. Murty

Abstract

3.1 Introduction

3.2 The Centering Strategy

3.3 Descent Step Using a Descent Direction

3.4 Descent Step Using the Touching Constraints

3.5 The Algorithm

3.6 Convergence Results

3.7 The Case When the Matrix D is Not Positive Definite

Bibliography

4. A General Framework for the Analysis of Sets of Constraints R. Caron and T. Traynor

Abstract

4.1 Introduction

4.2 The Set Covering Formulation

4.3 Random Sampling

Acknowledgement

Bibliography

5. Tolerance-based Algorithms for the Traveling Salesman Problem D. Ghosh, B. Goldengorin, G. Gutin

Abstract

5.1 Introduction

5.2 Some Relevant Concepts

5.2.1 The Relaxed Assignment Problem

5.2.2 Determining Tolerances for AP and RAP

5.2.3 The Contraction Procedure and a Greedy Algorithm

5.3 Tolerance-based Greedy Algorithms

5.4 Computational Experience

5.5 Summary and Future Research Directions

Bibliography

6. On the Membership Problem of the Pedigree Polytope T. S. Arthanari

Abstract

6.1 Introduction

6.1.1 Computational Complexity, Polytopes and Efficiency

6.2 Preliminaries & Notations

6.2.1 Rigid, Dummy arcs in a Capacited Transportation Problem

6.2.2 Definition of the Pedigree Polytope

6.2.3 Multistage Insertion and Related Results

6.3 Polytopes and Efficiency

6.3.0.1 Problems Related to Polytopes

6.3.1 Properties of the Polytope, conv(An)

6.4 Construction of the Layered Network N

6.5 Necessity of Fk Feasibility for Membership

6.6 Pedigree Packability

6.7 A Multicommodity Flow Problem to Check Member- ship

6.8 Computational Complexity of Checking the Necessary Condition

6.9 Concluding Remarks

Acknowledgements

Bibliography

7. Exact Algorithms for a One-defective Vertex Colouring Problem N. Achuthan, N. R. Achuthan and R.

Abstract

7.1 Introduction

7.2 Sequential Colouring Heuristics for k-DVCP

7.3 Implicit Enumeration Algorithms for 1–DVCP

7.4 Computational Performance of the Algorithms

Acknowledgement

Bibliography

8. Complementarity Problem involving a Vertical Block Matrix and its Solution using Neural Network M

Abstract

8.1 Introduction

8.2 Preliminaries

8.3 Main Results

8.4 Computing VLCP Solution Using the Neural Network Dynamics

8.4.1 Proposed Neural Network Dynamics

8.5 Simulation Results

Bibliography

9. Fuzzy Twin Support Vector Machines for Pattern Classi cation R. Khemchandani, Jayadeva and S. Cha

Abstract

9.1 Introduction

9.2 Support Vector Machines

9.3 Twin Support Vector Machines

9.4 Fuzzy Twin Support Vector Machines

9.5 Experimental Results

9.6 Concluding Remarks

Acknowledgements

Bibliography

10. An Overview of the Minimum Sum of Absolute Errors Regression S. C. Narula and J. F. Wellington

Abstract

10.1 Introduction

10.2 Computational Algorithms

10.3 Statistical Properties and Inference

10.4 Variable Selection

10.5 Coefficient of Determination

10.6 Other Results

10.7 Likelihood Displacement

10.8 Robustness

10.9 Multiple Criteria Linear Regression Using MSAE

10.10 Concluding Remarks

Bibliography

11. Hedging against the Market with No Short Selling S. A. Clark and C. Srinivasan

Abstract

11.1 Introduction

11.2 Securities Market Model

11.3 Fundamental Value

11.4 Trading Strategies

11.5 Hedging Prices

Bibliography

12. Mathematical Programming and Electrical Network Analysis II: Computational Linear Algebra throug

Abstract

12.1 Introduction

12.2 Electrical Network Analysis Procedures

12.2.1 Nodal Analysis

12.2.2 Loop Analysis

12.2.3 Hybrid Analysis

12.3 Experimental Results

12.4 A Proposal

12.5 Conclusion

Appendix: A variation of PCG

A.1 Modi ed CG

A.2 Modi ed Preconditioned CG

A.3 Justi cation for Modi ed Preconditioned CG

Bibliography

13. Dynamic Optimal Control Policy in Price and Quality for High Technology Product A. K. Bardhan an

Abstract

13.1 Introduction

13.2 Dynamic Diffusion of Demand

13.3 Model Development

13.4 Dynamic Optimization

13.5 Theoretical Results

13.6 Pricing and Quality Impact on Leapfrogging

13.7 Optimal Introduction Timing Strategy for Second Generation Product

13.8 Conclusions

Acknowledgement

Appendix

A. Optimal Pricing

B. Significance of Pricing and Quality in Leapfrogging

C. Optimal Introduction Timing Strategy

Bibliography

14. Forecasting for Supply Chain and Portfolio Management K. G. Murty

Abstract

14.1 Introduction

14.2 Costs of High Inventories and Shortages

14.3 Commonly used Techniques for Forecasting Demand

14.4 Parametric Methods for Forecasting Demand Distri- bution

14.4.1 Using Normal Distribution with updating of Ex- pected Value and Standard Deviation in each Pe

14.4.2 Using Normal Distribution with Updating of Ex- pected Value and Standard Deviation only when

14.4.3 Using Distributions other than Normal

14.5 A Nonparametric Method for Updating and Forecast- ing the Entire Demand Distribution

14.6 An Application of the Forecasting Method of Section 14.5 for computing Optimal Order Quantities

14.7 How to incorporate Seasonality in Demand into the Model

14.8 Portfolio Management

14.9 Variance as a Measure of Risk, and the Markovitz Model for Portfolio Optimization

14.10 Other Measures of Risk for Portfolio Optimization

14.11 Portfolio Management: Tracking the Distribution of Return from a Portfolio that is kept for a

14.12 A Model based on Statistical Learning to nd an Op- timum Portfolio

Bibliography

15. Variational Analysis in Bilevel Programming S. Dempe, J. Dutta and B. S. Mordukhovich

Abstract

15.1 Introduction

15.2 Tools from Variational Analysis

15.3 Partially Convex Lower-level Problems

15.4 Fully Convex Lower-level Problems

Acknowledgements

16. Game Engineering R. J. Aumann

Auctions:

Bibliography

Arbitration:

Traffic:

17. Games of Connectivity P. Dubey and R. Garg

Abstract

17.1 Introduction

17.2 Examples

17.2.1 Multicast Transmission

17.2.2 Unicast Transmission

17.2.3 Transmission of Layered Information

17.2.4 Transmission of Information Partitions

17.2.5 General Network with Controlled Edges

17.3 The Abstract Model

17.3.1 The Communications Network

17.3.2 Information

17.3.3 Location of Players and Public Facilities

17.3.4 Control of Edges

17.3.5 The Transmission of Information

17.3.6 The Reception of Information

17.3.7 The Cost of a Transmission

17.3.8 The Bene t from a Transmission

17.4 The Connectivity Game

17.5 The Growing Transmissions Property

17.6 Remarks

17.7 Appendix

17.7.1 Proof of Theorem 17.1

17.7.2 Proof of Theorem 17.2

Bibliography

18. A Robust Feedback Nash Equilibrium in a Climate Change Policy Game M. Hennlock

Abstract

18.1 Introduction

18.2 The Climate Models

18.2.1 Climate Change Impacts

18.3 Players and Payo s

18.3.1 Investor i 2 [1; n]

18.3.2 Policy Maker j 2 [1;N]

18.3.3 Game Formulations

18.4 Concluding Comments

18.5 Summary

18.6 Appendix

18.6.1 Appendix A.1 Proof of Proposition 1

18.6.2 Appendix A.2 Proof of Proposition 2

Bibliography

19. De Facto Delegation and Proposer Rules H. Imai and K. Yonezaki

Abstract

19.1 Introduction

19.2 Model and Result

19.3 Proof

19.4 FO rule and Discussion

19.5 Conclusion

Acknowledgements

Bibliography

20. The Bargaining Set in E ectivity Function D. Raza mahatolotra

20.1 Introduction

20.2 Definitions and Notations

20.3 Some Analysis of Cycles

20.4 Stability and Cycles

20.4.1 Comparison of the Bargaining Sets

20.4.2 The Zhou’s Bargaining Set

20.4.3 The Mass-Colell’s Bargaining Set

20.5 Annexe

Bibliography

21. Dynamic Oligopoly as a Mixed Large Game { Toy Market A. Wiszniewska-Matyszkiel

Abstract

21.1 Introduction

21.1.1 Large Games

21.2 Formulation of the Basic Model

21.2.1 Producers

21.2.2 Parents (and Children)

21.2.3 Market Clearing

21.3 Results

21.3.1 Case A: Two Periods with Dead-Season

21.3.2 Case B: Two Periods

21.3.3 Case C: Finitely Many Stages and Negligibility of Low Advertising Efforts

21.3.4 Case D: In nite Time Horizon and Negligibility of Low Advertising Efforts

21.4 Conclusions

Bibliography

22. On Some Classes of Balanced Games R. B. Bapat

Abstract

22.1 Introduction

22.2 Regression Games

22.3 Connectivity Games

Bibliography

23. Market Equilibrium for Combinatorial Auctions and the Matching Core of Nonnegative TU Games S. L

Abstract

23.1 Introduction

23.2 Combinatorial Auctions

23.3 Games with Transferable Utilities

23.4 Games with Transferable Utilities as Combinatorial Auctions

23.5 Market Equilibrium and Matching Cores

23.6 Discussion

Acknowledgements

Bibliography

24. Continuity, Manifolds, and Arrow’s Social Choice Problem K. Saukkonen

Abstract

24.1 Introduction

24.2 Continuity via Topological Manifolds

24.2.1 Background

24.2.2 Chickhilnisky’s Smooth Social Welfare Function

24.2.3 Illustrations of the Framework

24.2.4 Implications of the Manifold View

24.3 Manifolds and Arrovian Social Choice Systems

24.3.1 Simple Arrow-type Social Choice System

24.3.2 Market Mechanism and Welfare

24.3.3 Voting

24.3.4 Legislation

24.3.5 Arrow’s Abstract Theory of Collective Decision Making

24.4 Summary

Bibliography

25. On a Mixture Class of Stochastic Game with Ordered Field Property S. K. Neogy, A. K. Das, S. Sin

Abstract

25.1 Introduction

25.2 Preliminaries

25.3 Discounted Zero-sum SC/AR-AT Mixture Stochastic Game

25.4 Undiscounted Zero-sum SC/AR-AT Mixture Stochas- tic Game

25.5 Computation of Value Vector and Optimal Stationary Strategies for SC/AR-AT Mixture Class of Sto

Bibliography

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