## Mathematical Programming and Game Theory for Decision MakingThis edited book presents recent developments and state-of-the-art review in various areas of mathematical programming and game theory. It is a peer-reviewed research monograph under the ISI Platinum Jubilee Series on Statistical Science and Interdisciplinary Research. This volume provides a panoramic view of theory and the applications of the methods of mathematical programming to problems in statistics, finance, games and electrical networks. It also provides an important as well as timely overview of research trends and focuses on the exciting areas like support vector machines, bilevel programming, interior point method for convex quadratic programming, cooperative games, non-cooperative games and stochastic games. Researchers, professionals and advanced graduates will find the book an essential resource for current work in mathematical programming, game theory and their applications. Sample Chapter(s). Foreword (45 KB). Chapter 1: Mathematical Programming and its Applications in Finance (177 KB). Contents: Mathematical Programming and Its Applications in Finance (L C Thomas); Anti-Stalling Pivot Rule for Linear Programs with Totally Unimodular Coefficient Matrix (S N Kabadi & A P Punnen); A New Practically Efficient Interior Point Method for Convex Quadratic Programming (K G Murty); A General Framework for the Analysis of Sets of Constraints (R Caron & T Traynor), Tolerance-Based Algorithms for the Traveling Salesman Problem (D Ghosh et al.); On the Membership Problem of the Pedigree Polytope (T S Arthanari); Exact Algorithms for a One-Defective Vertex Colouring Problem (N Achuthan et al.); Complementarity Problem Involving a Vertical Block Matrix and Its Solution Using Neural Network Model (S K Neogy et al.); Fuzzy Twin Support Vector Machines for Pattern Classification (R Khemchandani et al.); An Overview of the Minimum Sum of Absolute Errors Regression (S C Narula & J F Wellington); Hedging Against the Market with No Short Selling (S A Clark & C Srinivasan); Mathematical Programming and Electrical Network Analysis II: Computational Linear Algebra Through Network Analysis (H Narayanan); Dynamic Optimal Control Policy in Price and Quality for High Technology Product (A K Bardhan & U Chanda); Forecasting for Supply Chain and Portfolio Management (K G Murty); Variational Analysis in Bilevel Programming (S Dempe et al.); Game Engineering (R J Aumann); Games of Connectivity (P Dubey & R Garg); A Robust Feedback Nash Equilibrium in a Climate Change Policy Game (M Hennlock); De Facto Delegation and Proposer Rules (H Imai & K Yonezaki); The Bargaining Set in Effectivity Function (D Razafimahatolotra); Dynamic Oligopoly as a Mixed Large Game OCo Toy Market (A Wiszniewska-Matyszkiel); On Some Classes of Balanced Games (R B Bapat); Market Equilibrium for Combinatorial Auctions and the Matching Core of Nonnegative TU Games (S Lahiri); Continuity, Manifolds, and Arrow''s Social Choice Problem (K Saukkonen); On a Mixture Class of Stochastic Games with Ordered Field Property (S K Neogy). Readership: Researchers, professionals and advanced students in mathematical programming, game theory, management sciences and computational mathematics. |

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### Contents

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

2 Antistalling Pivot Rule for Linear Programs with Totally Unimodular Coe cient Matrix S N Kabadi and A P Punnen | 15 |

3 A New Practically E cient Interior Point Method for Convex Quadratic Programming K G Murty | 21 |

4 A General Framework for the Analysis of Sets of Constraints R Caron and T Traynor | 33 |

5 Tolerancebased Algorithms for the Traveling Salesman Problem D Ghosh B Goldengorin G Gutin and G J ager | 47 |

6 On the Membership Problem of the Pedigree Polytope T S Arthanari | 61 |

7 Exact Algorithms for a Onedefective Vertex Colouring Problem N Achuthan N R Achuthan and R Collinson | 99 |

8 Complementarity Problem involving a Vertical Block Matrix and its Solution using Neural Network Model S K Neogy A K Das and P Das | 113 |

14 Forecasting for Supply Chain and Portfolio Management K G Murty | 231 |

15 Variational Analysis in Bilevel Programming S Dempe J Dutta and B S Mordukhovich | 257 |

16 Game Engineering R J Aumann | 279 |

17 Games of Connectivity P Dubey and R Garg | 287 |

18 A Robust Feedback Nash Equilibrium in a Climate Change Policy Game M Hennlock | 305 |

19 De Facto Delegation and Proposer Rules H Imai and K Yonezaki | 327 |

20 The Bargaining Set in E ectivity Function D Raza mahatolotra | 339 |

21 Dynamic Oligopoly as a Mixed Large Game Toy Market A WiszniewskaMatyszkiel | 369 |

9 Fuzzy Twin Support Vector Machines for Pattern Classi cation R Khemchandani Jayadeva and S Chandra | 131 |

10 An Overview of the Minimum Sum of Absolute Errors Regression S C Narula and J F Wellington | 143 |

11 Hedging against the Market with No Short Selling S A Clark and C Srinivasan | 169 |

Computational Linear Algebra through Network analysis H Narayanan | 187 |

13 Dynamic Optimal Control Policy in Price and Quality for High Technology Product A K Bardhan and U Chanda | 213 |

22 On Some Classes of Balanced Games R B Bapat | 391 |

23 Market Equilibrium for Combinatorial Auctions and the Matching Core of Nonnegative TU Games S Lahiri | 401 |

24 Continuity Manifolds and Arrows Social Choice Problem K Saukkonen | 415 |

25 On a Mixture Class of Stochastic Game with Ordered Field Property S K Neogy A K Das S Sinha and A Gupta | 451 |

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advertising algorithm analysis Arrovian social Arrow assume assumption bilevel programming block matrix Chichilnisky coalition coeﬃcient colouring combinatorial computational consider constraints convex corresponding cost deﬁned deﬁnition denote diﬀerent diﬀerential distribution edges eﬀect effectivity function eﬃcient equations equivalent estimates feasible feedback Nash ﬁeld ﬁnd ﬁnite ﬁrm ﬁrst ﬁxed ﬂow Game Theory given graph greedy algorithms Indian Statistical Institute inﬁnite investors Lemma linear complementarity problem linear programming lower-level problem manifold market equilibrium Mathematical Programming maximal method minimal MSAE regression Narula Nash equilibrium Neogy node observations obtained Operations Research parameter partition payoﬀ pedigree players policy maker polytope portfolio Proof Proposition radiative forcing result robust Section social choice problems social welfare function solving Statistical stochastic game strategies structure subset supermodular Support Vector Machines Suppose Theorem theory tion topological vector vertex vertical block matrix zero