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Kim C. Border

Fixed Point Theorems With Applications to Economics and Game Theory

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ISBN: 0521388082, 9780521388085
Издательство: Cambridge University Press
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 askedunder 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 thepreferences 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...