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Two‐Aggregate Games: Demonstration Using a Production–Appropriation Model
Author(s) -
Cornes Richard,
Hartley Roger,
Tamura Yuji
Publication year - 2019
Publication title -
the scandinavian journal of economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.725
H-Index - 64
eISSN - 1467-9442
pISSN - 0347-0520
DOI - 10.1111/sjoe.12257
Subject(s) - appropriation , aggregate (composite) , production (economics) , scope (computer science) , consistency (knowledge bases) , economics , mathematical economics , nash equilibrium , computer science , resource allocation , microeconomics , mathematical optimization , mathematics , artificial intelligence , market economy , philosophy , linguistics , materials science , programming language , composite material
We expand the scope of the two‐aggregate method by applying it to a situation in which many heterogeneous players are free to contribute to both aggregates. Such situations naturally arise in various resource allocation problems. Hence, our method is useful in many applications. A production–appropriation model is employed to illustrate how the problem of establishing the Nash equilibrium can be reduced from solving n >2 best‐response functions in n unknowns to solving two consistency conditions in two unknowns. We then conduct a comparative static exercise that the conventional approach could not handle easily, if at all, to demonstrate the power of our method.