Discrete convex analysis: A tool for economics and game theory
This paper presents discrete convex analysis as a tool for use in economics and game theory. Discrete convex analysis is a new framework of discrete mathematics and optimization, developed during the last two decades. Recently, it has been recognized as a powerful tool for analyzing economic...
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| Format: | Article |
| Language: | English |
| Published: |
Society for the Promotion of Mechanism and Institution Design
2016-12-01
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| Series: | Journal of Mechanism and Institution Design |
| Subjects: | |
| Online Access: |
http://www.mechanism-design.org/arch/v001-1/p_05.pdf
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| Summary: | This paper presents discrete convex analysis as a tool for use in economics and
game theory. Discrete convex analysis is a new framework of discrete mathematics and optimization,
developed during the last two decades. Recently,
it has been recognized as a powerful tool for analyzing economic or game
models with indivisibilities. The main feature of discrete convex analysis is
the distinction of two convexity concepts, M-convexity and L-convexity, for
functions in integer or binary variables, together with their conjugacy relationship.
The crucial fact is that M-concavity in its variant is equivalent to the gross
substitutes property in economics. Fundamental theorems in discrete convex
analysis such as the M-L conjugacy theorems, discrete separation theorems
and discrete fixed point theorems yield structural results in economics such as
the existence of equilibria and the lattice structure of equilibrium price vectors.
Algorithms in discrete convex analysis provide iterative auction algorithms for
finding equilibria. |
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| ISSN: | 2399-844X 2399-8458 |