Abstract economy¶

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.

Version: v1 · 2026-09-28 · History
Domain-specific #: 7830
Domain group: Social Sciences
Origin domain: Economics & Finance
Subdomains: Mathematical Economics, General Equilibrium Theory → Economics & Finance

Core Idea¶

Abstract economy is treated here as the recurring mathematical economics identity summarized by this source-grounded definition: 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. 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.

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Market-and-Game World

Grown-ups who study money and games made one big pretend world that works for both trading at a market and playing a game. In that pretend world they look for a resting spot where nobody can do better by changing what they do on their own. They proved that, when the pretend world follows certain rules, such a resting spot really exists.

One Model for Markets and Games

Economists have a math model for a market where people trade goods, and game experts have a math model for games where players pick moves. An abstract economy is a bigger model that includes both as special cases. In it, economists look for an equilibrium - a situation where no one wants to change their choice. A mathematician named Gerard Debreu invented it in 1952 and proved that, under certain conditions, an equilibrium is guaranteed to exist. Later that proof helped show that whole markets can balance out.

Generalized N-Person Game

An abstract economy, also called a generalized N-person game, is a model in theoretical economics that generalizes two standard models at once: the exchange economy of microeconomics and the game of game theory. Its equilibrium concept likewise generalizes both market equilibrium (called Walrasian equilibrium, where prices balance supply and demand) and Nash equilibrium (where no player gains by changing strategy alone). Gerard Debreu introduced it in 1952 and proved that an equilibrium exists. Kenneth Arrow, who gave it the name 'abstract economy', and Debreu then used that result to prove that competitive equilibrium exists in the Arrow-Debreu model. Later, Shafer and Sonnenschein extended the results to agents whose preferences aren't fully consistent.

In mathematical economics, an abstract economy (or generalized N-person game) is a model that contains both the exchange economy and the N-person game as special cases. Its key structural feature is that what each agent may choose is not fixed in advance but can depend on the choices of the others, which lets market budget constraints and strategic interaction live in one framework. An equilibrium of an abstract economy generalizes both a Walrasian (competitive) equilibrium and a Nash equilibrium. Gerard Debreu introduced the concept in 1952 as the generalized N-person game and proved existence of equilibrium. Arrow and Debreu, with Arrow renaming it the abstract economy, then used this existence theorem to establish existence of Walrasian equilibrium in the Arrow-Debreu model. Shafer and Sonnenschein later extended both theorems to agents with non-transitive and non-complete preferences, i.e. beyond standard rationality assumptions.

Scope of Application¶

Abstract economy with utility functionsThe general case. A utility function: Ui: X\to \mathbb{R} , representing the utility that the agent receives from each combination of choices.
Equilibrium. Each utility function Ui is continuous in x and quasi-concave in xi.
Equilibrium. The continuity conditions on the utility functions can be weakened as follows.
Equilibrium. Each utility function Ui is quasi-concave in xi , upper semi-continuous in x , and graph continuous.
Equilibrium. Each utility function Ui is quasi-concave in xi , upper semi-continuous in x , and the function Wi(x{-i}) := \max{xi}Ui(xi,x{-i}) [which is defined since Ui is upper.

Clarity¶

A clear use of Abstract economy names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is 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.

Manages Complexity¶

Abstract economy compresses multiple mathematical economics details into a stable diagnostic relation. The source shows both the central mechanism—note that the utility of a consumer depends only on his own consumption, rather than on the entire allocation.—and the practical consequence—in the proof we assumed that Vi depends only on yi , but this assumption is not really needed: the proof remains valid even if the utility depends on.

Abstract Reasoning¶

Type the carrier. Identify the mathematical economics entities to which the claim applies.
State the relation. Use the source-grounded identity: 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.
Check operation and conditions. Given an (N-1)-agent exchange economy, we define an N-agent abstract economy by adding a special agent called the market maker or market player.

Knowledge Transfer¶

Within the home domain. Knowledge about Abstract economy transfers literally when a new case preserves the same carrier type, relation, and recognition test. A utility function: Ui: X\to \mathbb{R} , representing the utility that the agent receives from each combination of choices. Each utility function Ui is continuous in x and quasi-concave in xi. Beyond the home domain. No canonical parent is asserted for Abstract economy. An outside case receives the specialist name only when the same typed roles and rejection conditions can be filled literally; otherwise the comparison remains an analogy pending later graph densification.

Neighborhood in Abstraction Space¶

Abstract economy sits in a crowded region of the domain-specific corpus (38^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Market Structure & Competition Models (7 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08