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In theoretical economics, an abstract economy (also called a generalized N-person game) is a model that generalizes both the standard model of an exchange economy in microeconomics, and the standard model of a game in game theory. An equilibrium in an abstract economy generalizes both a Walrasian equilibrium in microeconomics, and a Nash equilibrium in game-theory.
The concept was introduced by Gérard Debreu in 1952. He named it generalized N-person game, and proved the existence of equilibrium in this game.[1] Later, Debreu and Kenneth Arrow (who renamed the concept to abstract economy) used this existence result to prove the existence of a Walrasian equilibrium (aka competitive equilibrium) in the Arrow–Debreu model.[2] Later, Shafer and Sonnenschein extended both theorems to irrational agents - agents with non-transitive and non-complete preferences.[3][4]
^Debreu, Gerard (1952-10-01). "A Social Equilibrium Existence Theorem". Proceedings of the National Academy of Sciences. 38 (10): 886–893. Bibcode:1952PNAS...38..886D. doi:10.1073/pnas.38.10.886. ISSN 0027-8424. PMC 1063675. PMID 16589195.
^Arrow, Kenneth J.; Debreu, Gerard (1954). "Existence of an Equilibrium for a Competitive Economy". Econometrica. 22 (3): 265–290. doi:10.2307/1907353. JSTOR 1907353.
^Shafer, Wayne; Sonnenschein, Hugo (1975-12-01). "Equilibrium in abstract economies without ordered preferences" (PDF). Journal of Mathematical Economics. 2 (3): 345–348. doi:10.1016/0304-4068(75)90002-6. hdl:10419/220454. ISSN 0304-4068.
^https://arxived.org/pdfs/files/425be847d31d3cc9665d00b8f0585038.pdf[permanent dead link]
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