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A Unified Approach to p-Dominance and its Generalizations in Games with Strategic Complements and Substitutes

Anne-Christine Barthel, Eric Hoffman and Tarun Sabarwal ()
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Anne-Christine Barthel: Department of Economics, West Texas A&M University, Canyon, TX, 79016, USA
Eric Hoffman: Department of Economics, West Texas A&M University, Canyon, TX, 79016, USA

No 202109, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics

Abstract: The concepts of p-dominance and its generalizations are useful to understand equilibrium selection and equilibrium stability in games. We prove that in games with strategic complements, games with strategic substitutes, and games with combinations of both, these concepts are logically equivalent to pure strategy Nash equilibria in a transformed game of complete information. The transformation process is easy to follow and implement and retains a natural connection to the original game. Therefore, our results make these solution concepts more tractable and accessible, and this is shown in many applications. The connection to Nash equilibrium helps us prove new results about the structure of classes of such solution concepts. Similar to the case of Nash equilibrium, these classes are complete lattices in games with strategic complements, but are totally unordered when we deviate from this case.

Keywords: p-dominance; p-best response set; minimal p-best response set; strategic complements; strategic substitutes (search for similar items in EconPapers)
JEL-codes: C62 C72 (search for similar items in EconPapers)
Pages: 38 pages
Date: 2021-02
New Economics Papers: this item is included in nep-gth
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