Fixed Point Theorems with Applications to Economics and Game Theory (Paperback)

Kim C. Border

ISBN 10: 0521388082 / ISBN 13: 9780521388085

Published by Cambridge University Press, Cambridge, 1989

About this Item

Paperback. One of the problems in economics to which economists have devoted a considerable amount of attention in recent years has been to ensure consistency in the models they employ. Assuming markets to be generally in some state of equilibrium, it must be asked under what circumstances such an equilibrium is possible. The fundamental mathematical tools used to address this concern are fixed point theorems. These outline the conditions under which sets of assumptions have a solution. This book gives the reader access to the mathematical techniques involved and goes on to apply fixed point theorems to proving the existence of equilibria for economics and for cooperative and non-cooperative games. Special emphasis is given to economics and games in cases where the preferences of agents may not be transitive. In addition, the author presents new proofs of old results in order to further clarify the results. He also proposes new results, notably in the last chapter, that refer to the core of a game without transitivity. This book will be useful as a text or reference work for mathematical economists and graduate and advanced undergraduate students. Markets are assumed to be in a state of equilibrium. Fixed point theorems explain the circumstances of equilibrium. This book demonstrates the mathematical techniques involved and applies them to co-operative and noncooperative games. This book will be useful as a text or reference work for mathematical economists, graduate and advanced undergraduate students. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Seller Inventory # 9780521388085

Bibliographic Details

• Title: Fixed Point Theorems with Applications to Economics and Game Theory (Paperback)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 1989
• Language: English
• ISBN 10: 0521388082
• ISBN 13: 9780521388085
• Binding: Paperback
• Condition: new

About this title

Synopsis

One of the problems in economics that economists have devoted a considerable amount of attention in prevalent years has been to ensure consistency in the models they employ. Assuming markets to be generally in some state of equilibrium, it is asked under what circumstances such equilibrium is possible. The fundamental mathematical tools used to address this concern are fixed point theorems: the conditions under which sets of assumptions have a solution. This book gives the reader access to the mathematical techniques involved and goes on to apply fixed point theorems to proving the existence of equilibria for economics and for co-operative and noncooperative games. Special emphasis is given to economics and games in cases where the preferences of agents may not be transitive. The author presents topical proofs of old results in order to further clarify the results. He also proposes fresh results, notably in the last chapter, that refer to the core of a game without transitivity. This book will be useful as a text or reference work for mathematical economists and graduate and advanced undergraduate students.

Book Description

An introduction to fixed point theory, a body of mathematical techniques for proposing conditions under which sets of assumptions (underlying economic models) have solutions.