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Fixed Point Theorems with Applications to Economics and Game Theory

Author

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  • Border,Kim C.

Abstract

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.

Suggested Citation

  • Border,Kim C., 1990. "Fixed Point Theorems with Applications to Economics and Game Theory," Cambridge Books, Cambridge University Press, number 9780521388085.
    • Handle: RePEc:cup:cbooks:9780521388085
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    Cited by:

    1. Renou, Ludovic & Atakan, Alp & Ekmekci, Mehmet, 2021. "Cross-verification and Persuasive Cheap Talk," CEPR Discussion Papers 16801, C.E.P.R. Discussion Papers.
    2. Abd EL-Monsef, M.E. & Abu-Donia, H.M. & Abd-Rabou, Kh., 2009. "New types of common fixed point theorems in 2-metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1435-1441.
    3. Konstantinos Eleftheriou & Iliya Komarev & Paul Klumpes, 2023. "Regulating the Market for Audit Services: A Game Theoretic Approach," Abacus, Accounting Foundation, University of Sydney, vol. 59(3), pages 697-734, September.
    4. Ahmed, M.A., 2009. "A common fixed point theorem for expansive mappings in 2-metric spaces and its application," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2914-2920.

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