Supermodularity & Complementarity

Preface xi Chapter 1 Introduction 3(4) Chapter 2 Lattices, Supermodular Functions, and Related Topics 7(87) 2.1 Introduction 7(4) 2.2 Partially Ordered Sets and Lattices 11(18) 2.2.1 Definitions, Notation, and Some Basic Properties 11(6) 2.2.2 Sublattice Structure 17(12) 2.3 Completeness and Topological Properties 29(3) 2.4 Induced Set Ordering 32(6) 2.5 Fixed Points 38(4) 2.6 Supermodular Functions on a Lattice 42(24) 2.6.1 Characterization and Complementarity 42(7) 2.6.2 Transformations 49(9) 2.6.3 Ordinal Generalizations 58(6) 2.6.4 Log-Supermodularity 64(2) 2.7 Maximizing a Supermodular Function 66(8) 2.7.1 Sets of Maximizers 66(4) 2.7.2 Preservation of Supermodularity 70(4) 2.8 Increasing Optimal Solutions 74(18) 2.8.1 Sufficient Conditions 74(9) 2.8.2 Necessary Conditions 83(9) 2.9 Complementarity Equivalences 92(2) Chapter 3 Optimal Decision Models 94(81) 3.1 Introduction 94(1) 3.2 Matching 95(7) 3.3 Comparative Statics of the Firm 102(23) 3.3.1 Model of the Firm 103(1) 3.3.2 Sufficient Conditions 104(17) 3.3.3 Necessary Conditions 121(4) 3.4 Transportation and Transshipment Problems 125(6) 3.4.1 Transportation Problem 125(4) 3.4.2 Transshipment Problem 129(2) 3.5 Dynamic Economic Lot Size Production Models, Acyclic Networks 131(7) 3.5.1 Acyclic Networks 132(2) 3.5.2 Dynamic Economic Lot Size Production Models 134(4) 3.6 Production Planning 138(4) 3.7 Minimum Cuts, Maximum Closures, and the Selection Problem 142(9) 3.7.1 Minimum Cut Problem 143(3) 3.7.2 Maximum Closure Problem 146(2) 3.7.3 Selection Problem 148(2) 3.7.4 Equivalent Combinatorial Structures 150(1) 3.8 Myopic Decisions 151(7) 3.8.1 General Conditions 152(3) 3.8.2 Dynamic Selection Problem 155(3) 3.9 Markov Decision Processes and Property-Inducing Stochastic Transformations 158(11) 3.9.1 Property-Inducing Stochastic Transformations 159(4) 3.9.2 Markov Decision Processes 163(6) 3.10 Stochastic Inventory Problems and Supermodularity-Preserving Stochastic Transformations 169(6) 3.10.1 Supermodularity-Preserving Stochastic Transformations 169(1) 3.10.2 Stochastic Inventory Problems 170(5) Chapter 4 Noncooperative Games 175(32) 4.1 Introduction 175(4) 4.2 Existence of an Equilibrium Point, Parametric Properties 179(6) 4.3 Algorithms for Approximating an Equilibrium Point 185(10) 4.3.1 Round-Robin Optimization 185(5) 4.3.2 Simultaneous Optimization 190(5) 4.4 Examples of Supermodular Games 195(12) 4.4.1 Pricing Game with Substitute Products 196(2) 4.4.2 Production Game with Complementary Products 198(1) 4.4.3 Multimarket Oligopoly 199(1) 4.4.4 Arms Race Game 200(1) 4.4.5 Trading Partner Search Game 201(1) 4.4.6 Optimal Consumption Game with Multiple Products 202(1) 4.4.7 Facility Location Game 203(1) 4.4.8 Minimum Cut Game 204(3) Chapter 5 Cooperative Games 207(56) 5.1 Introduction 207(4) 5.2 Convex Games 211(27) 5.2.1 The Core and the Greedy Algorithm 211(10) 5.2.2 Games with a Parameter 221(2) 5.2.3 Structure of the Core 223(15) 5.3 Examples of Convex Games 238(6) 5.3.1 Monopoly Firm 238(2) 5.3.2 Monotonic Surplus Sharing 240(1) 5.3.3 Aircraft Landing Fee Game 241(2) 5.3.4 Trading Game 243(1) 5.4 Activity Optimization Games 244(4) 5.5 Examples of Activity Optimization Games 248(10) 5.5.1 General Welfare Game 249(1) 5.5.2 Production Game with Common Procurement of Inputs 250(2) 5.5.3 Investment and Production Game 252(1) 5.5.4 Activity Selection Game 253(3) 5.5.5 Waste Disposal Game 256(2) 5.6 Games with Complementarities That Are Not Convex Games 258(5) 5.6.1 Network Design Game 258(3) 5.6.2 Max-Min Game 261(2) Bibliography 263(6) Index 269