Characterizing Robust Solutions to Monotone Games

Anne-Christine Barthel, Eric Hoffman and Tarun Sabarwal
Additional contact information
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 202012, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics

Abstract: In game theory, p-dominance and p-best response sets serve as important robustness solution concepts by allowing for deviations from the stringent common knowledge requirements of Nash equilibrium. However, solving for such sets remains largely intractable beyond the simplest of settings. The contributions of this paper are twofold: First, in monotone games, (which include the broad class of supermodular games, submodular games, and their combinations,) we show that these concepts can be characterized in terms of pure strategy Nash equilibria in an auxiliary game of complete information. This makes it considerably easier to compute such sets, facilitating their broader use. Second, these characterizations lead to new results about the structure of entire classes of such solution concepts, including minimal p-best response (p-MBR) sets, which generalize well known results for pure strategy Nash equilibria. In games with strategic complements, these classes are complete lattices. More generally, they are totally unordered. Several examples highlight the results.

Keywords: Strategic complements; Strategic substitutes; Monotone games; p-dominance; p-best response set (search for similar items in EconPapers)
JEL-codes: C60 C70 C72 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2020-07
New Economics Papers: this item is included in nep-gth, nep-mic and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Characterizing robust solutions in monotone games (2022)
Working Paper: Characterizing Robust Solutions in Monotone Games (2021)
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