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Characterizing Robust Solutions in Monotone Games

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

No 202121, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics

Abstract: In game theory, p-dominance and its set-valued generalizations serve as important robust solution concepts. We show that in monotone games, (which include the broad classes of super-modular games, sub-modular games, and their combinations,) these concepts can be characterized in terms of pure strategy Nash equilibria in an auxiliary game of complete information. The auxiliary game is constructed in a transparent manner that is easy to follow and retains a natural connection to the original game. Our results show explicitly how to map these concepts to a corresponding Nash equilibrium thereby identifying a new bijection between robust solutions in the original game and equilibrium notions in the auxiliary game. Moreover, our characterizations lead to new results about the structure of entire classes of such solution concepts. In games with strategic complements, these classes are complete lattices. More generally, they are totally unordered. We provide several examples to highlight these results.

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: 39 pages
Date: 2021-02, Revised 2021-10
New Economics Papers: this item is included in nep-gth and nep-mic
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Working Paper: Characterizing Robust Solutions to Monotone Games (2020) Downloads
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