Characterizing Robust Solutions to Monotone Games
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 202012, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics
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
New Economics Papers: this item is included in nep-gth, nep-mic and nep-ore
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Working Paper: Characterizing Robust Solutions in Monotone Games (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:kan:wpaper:202012
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