Leseprobe
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Supermodularity and Complementarity
Donald M. Topkis
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Sozialwissenschaften, Recht, Wirtschaft / Wirtschaft
Beschreibung
The economics literature is replete with examples of monotone comparative statics; that is, scenarios where optimal decisions or equilibria in a parameterized collection of models vary monotonically with the parameter. Most of these examples are manifestations of complementarity, with a common explicit or implicit theoretical basis in properties of a super-modular function on a lattice. Supermodular functions yield a characterization for complementarity and extend the notion of complementarity to a general setting that is a natural mathematical context for studying complementarity and monotone comparative statics. Concepts and results related to supermodularity and monotone comparative statics constitute a new and important formal step in the long line of economics literature on complementarity.
This monograph links complementarity to powerful concepts and results involving supermodular functions on lattices and focuses on analyses and issues related to monotone comparative statics. Don Topkis, who is known for his seminal contributions to this area, here presents a self-contained and up-to-date view of this field, including many new results, to scholars interested in economic theory and its applications as well as to those in related disciplines. The emphasis is on methodology. The book systematically develops a comprehensive, integrated theory pertaining to supermodularity, complementarity, and monotone comparative statics. It then applies that theory in the analysis of many diverse economic models formulated as decision problems, noncooperative games, and cooperative games.
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Duality (optimization), Initial condition, Price elasticity of demand, Greedy algorithm, Marginal Cost Of Production, Markov decision process, Direct product, Feasible region, Power set, Monotonic function, Subset, Utility, Equilibrium point, Characteristic function (probability theory), Maximum flow problem, Monotone comparative statics, Theorem, Maximal element, Probability measure, Present value, Extreme point, Maxima and minima, Pointwise, Ellipsoid method, Cost curve, Economic problem, Product topology, Weight function, Topology, Total cost, N-vector, Cooperative game, Shapley value, Infimum and supremum, Cobb–Douglas production function, Convex combination, Function (mathematics), Permutation, Sensitivity analysis, Indicator function, Perturbation function, Linear inequality, Mathematical optimization, Net profit, Subadditivity, Special case, Demand modeling, Marginal cost, Decision problem, Stochastic, Assignment problem, Optimal decision, Optimization problem, Markov process, Marginal value, Probability distribution, Binary relation, Variable (mathematics), Marginal utility, Supermodular function, Parameter, Partially ordered set, Conditional probability distribution, Giffen good, Dynamic programming, Summation, Competitive Pricing, Upper and lower bounds, Transitive relation, Loss function