Minimally incomplete sampling and convergence of adaptive play in $$2\times 2$$ 2 × 2 games

Ethan Holdahl () and Anne van den Nouweland ()
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Ethan Holdahl: University of California
Anne van den Nouweland: University of Oregon

Economic Theory Bulletin, 2024, vol. 12, issue 1, No 1, 14 pages

Abstract: Abstract Adaptive learning explains how conventions emerge in populations in which players sample a sufficiently small portion of the recent plays and best reply to those samples. We establish that in $$2\times 2$$ 2 × 2 coordination games any degree of incomplete sampling is sufficient for a convention to be established and that the degree of sampling does not affect which conventions are most likely to emerge in the long run. Thus, the bound that players sample at most half of the plays available to them, which is prevalent in the large body of work that uses adaptive learning to examine which conventions emerge in a variety of games, is unnecessarily strict.

Keywords: Adaptive play; Incomplete sampling; Conventions; Stochastic stability (search for similar items in EconPapers)
JEL-codes: C72 C73 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s40505-024-00262-0

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