Open AccessIterated weak dominance and interval‐dominance supermodular games
Author(s) -
Sobel Joel
Publication year - 2019
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te2904
Subject(s) - dominance (genetics) , mathematical economics , iterated function , mathematics , interval (graph theory) , stochastic dominance , economics , combinatorics , mathematical optimization , biology , mathematical analysis , biochemistry , gene
This paper extends Milgrom and Robert's treatment of supermodular games in two ways. It points out that their main characterization result holds under a weaker assumption. It refines the arguments to provide bounds on the set of strategies that survive iterated deletion of weakly dominated strategies. I derive the bounds by iterating the best‐response correspondence. I give conditions under which they are independent of the order of deletion of dominated strategies. The results have implications for equilibrium selection and dynamic stability in games.