Economic Theory of Fuzzy Equilibria: An Axiomatic Analysis

ISBN-13: 9783642799518 / Angielski / Miękka / 2011 / 180 str.

Antoine Billot

Opis

Fuzzy set theory, which started not much more than 20 years ago as a generalization of classical set theory, has in the meantime evolved into an area which scientifically, as well as from the point of view of applications, is recognized as a very valuable contribution to the existing knowledge. This book provides a remarkable contribution to Fuzzy Economics and presents the state of the art in fuzzy theory of value, namely the aggregated model of microeconomics with fuzzy behaviours. It presents an analysis of classical problems with new tools which lead to interesting results.

Spis treści

General Introduction.- 1 Individual Fuzzy Relation of Preference.- 1.1 The Fuzzy Binary Relation of Preference.- 1.1.1 Binary Relation and Fuzzy Binary Relation.- 1.1.2 The Fuzzy Preference and its Properties.- 1.2 The Indifference Paradox.- 1.2.1 Reflexivity and Indifference.- 1.2.2 The Axiomatic Solution.- 1.2.3 Solution.- 1.3 Fuzzy Utility Function on a Countable Set.- 1.3.1 Subrelations of Similitude.- 1.3.2 The Transition Operator.- 1.3.3 Utility and Fuzzy Reflexivity.- 1.3.4 Totally Ordered Fuzzy Topological Space.- 1.3.5 A Fuzzy Utility Function.- 1.4 Fuzzy Utility Function on a Convex Set.- 1.4.1 Assumptions on X.- 1.4.2 The Associated Fuzzy Set Xf.- 1.4.3 Analysis of Assumptions.- 1.4.4 Continuity of Fuzzy Preferences.- 1.4.5 Assumption of Continuity for Fuzzy Preferences.- 1.4.6 Preliminary Results.- 1.4.7 Extension of v(.) to u(.) on X.- 1.5 A New Proof for Fuzzy Utility.- 1.5.1 New Definitions and Notations.- 1.5.2 Two Representation Lemmas.- 1.5.3 A Third Representation Theorem.- 1.5.4 Some Concluding Remarks.- 2 Aggregation of Fuzzy Preferences.- 2.1 Arrovian Dictator and Fuzzy Preferences.- 2.1.1 Imprecise Behavior and Fuzzy Individual Preferences.- 2.1.2 Fuzzy Preferences and Collective Decision : Arrow’s Axioms.- 2.1.3 Proof of the Dictator Theorem with Fuzzy Preferences.- 2.2 Fuzzy Coalitions and Democracy.- 2.2.1 Axioms of May’s Theorem.- 2.2.2 Generalized Theorem: Arrow versus May.- Annexes.- 3 Fuzzy Games.- 3.1 Fixed Points and Nash-Equilibrium.- 3.1.1 Fixed Points and Fuzzy Universe.- 3.1.2 Nash-Equilibria for Fuzzy Games.- 3.2 Prudent Behavior and Equilibria.- 3.2.1 Lexicographic Preorder and Continuity.- 3.2.2 Noncooperative Fuzzy Ordinal Game.- 3.2.3 Strategic Utility Function.- 3.2.4 Prudent Equilibria and Fuzzy Nash-Equilibria.- 3.3 Cooperative Fuzzy Games.- 3.3.1 f-Convexity and Fuzzy Preorders.- 3.3.2 Nonemptiness of the Peripheral Core.- 4 Fuzzy General Equilibrium.- 4.1 Tasks and Quasi Wage-Rates.- 4.1.1 The Different Approaches of Ability.- 4.1.2 Task, Quasi Wage-Rate and Partial Competition..- 4.1.3 A Labor-Commodities-Economy.- 4.1.4 A Fuzzy LCE.- 4.1.5 The Method for Fuzzy Optimization.- 4.2 The Existence of a Fuzzy General Equilibrium.- 4.2.1 A Private Ownership LCE.- 4.2.2 A General Fuzzy Equilibrium (à la Ponsard).- 4.2.3 Existence of Equilibria for a LCE à la Ponsard.- 4.2.4 Existence of a General Equilibrium in a Pure LCE.- 5 Underemployment Fuzzy Equilibrium.- 5.1 Existence of an Underemployment Equilibrium.- 5.1.1 Voluntary Unemployment and Walrasian Equilibrium Involuntary Unemployment.- 5.1.2 The Consumer-Worker’s Behavior.- 5.1.3 General Model of a Pure LCE.- 5.2 Involuntary Unemployment and Dominated Irrationality.- 5.2.1 Preliminary Remarks.- 5.2.2 Fuzzy Preference and Involuntary Unemployment.- 5.2.3 The Walrasian Equilibrium Involuntary Unemployed Worker’s Behavior.- 5.2.4 Voluntary and Involuntary Unemployed Workers.- 6 Fuzzy Economics: An Overview.- 6.1 The Birth of RPA.- 6.2 Preference Theory within RPA.- 6.3 Towards a Fuzzy Theory of Value.- 6.4 RPB and RPC Instrumentalism.- 6.5 Outlets for EP.- General Conclusion.- References.