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Nikolai S. Kukushkin
''Monotone comparative statics on semilattices''
( 2021, Vol. 41 No.3 )
This paper examines to what extent monotone comparative statics analysis in the style of Milgrom and Shannon (1994) can be extended from lattices to semilattices (e.g., budget sets). A condition on preference orderings is found which is necessary and sufficient for a monotone response of the optimal choice from every subsemilattice to a perturbation of the preferences satisfying an appropriate single crossing condition. A strategic game model related to the consumption of positional goods is formulated where Nash equilibrium exists because the players' preferences satisfy our condition.
Keywords: Semilattice, Monotone comparative statics, Single crossing, Strategic complementarities, Nash equilibrium
JEL: C7 - Game Theory and Bargaining Theory
D1 - Household Behavior: General
Manuscript Received : Feb 28 2021 Manuscript Accepted : Sep 17 2021

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