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<p>Adaptive learning dynamics have been widely studied in monotone games. By assuming that players eventually choose undominated responses to past play, these processes are intrinsically backwards-looking. However, it is also reasonable to assume that players are able to anticipate the backwards-looking behavior of their opponents, resulting in forward-looking dynamics which have largely been ignored in this literature. Using a cognitive hierarchy framework, we show that the limits of all <i>k</i>-level adaptive learning dynamics, which allow for <i>k</i> levels of such forward-looking behavior and subsume adaptive dynamics when <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11238_2025_10038_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(k=1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, fall within the smallest interval containing all serially undominated strategies, and hence converge to the unique serially undominated equilibrium in dominance solvable games. Using over 1200 rounds of experimental duopoly data from Oechssler et al. (J Econ Sci Assoc 2:13–21, 2016a; From imitation to collusion: a replication [dataset], 2016b. <a href="https://doi.org/10.11588/data/10075">https://doi.org/10.11588/data/10075</a>), we find not only that the <i>k</i>-level model is highly consistent with observed behavior, but our findings also suggest that allowing for higher levels of reasoning has an explanatory advantage over traditional adaptive dynamics.</p>

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k-level forward-looking dynamics in monotone games: theory and evidence

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • Anne-Christine Barthel,
  • Eric Hoffmann

摘要

Adaptive learning dynamics have been widely studied in monotone games. By assuming that players eventually choose undominated responses to past play, these processes are intrinsically backwards-looking. However, it is also reasonable to assume that players are able to anticipate the backwards-looking behavior of their opponents, resulting in forward-looking dynamics which have largely been ignored in this literature. Using a cognitive hierarchy framework, we show that the limits of all k-level adaptive learning dynamics, which allow for k levels of such forward-looking behavior and subsume adaptive dynamics when \(k=1\) k = 1 , fall within the smallest interval containing all serially undominated strategies, and hence converge to the unique serially undominated equilibrium in dominance solvable games. Using over 1200 rounds of experimental duopoly data from Oechssler et al. (J Econ Sci Assoc 2:13–21, 2016a; From imitation to collusion: a replication [dataset], 2016b. https://doi.org/10.11588/data/10075), we find not only that the k-level model is highly consistent with observed behavior, but our findings also suggest that allowing for higher levels of reasoning has an explanatory advantage over traditional adaptive dynamics.