Depth of Reasoning Models with Sophisticated Agents
Peter Moffatt (),
Ganna Pogrebna and
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Ganna Pogrebna: The Alan Turing Institute, The University of Sydney
Graciela Zevallos-Porles: School of Economics, University of East Anglia, Norwich.
No 20-06, Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) from School of Economics, University of East Anglia, Norwich, UK.
In the context of guessing games, we propose the Sophisticated Reasoning Model (SRM) which includes a â€œsophisticatedâ€ type. A parameter ps represents the proportion of sophisticated players in the population. Asophisticated player is one who forms a belief (eps) of the proportion of the population who are sophisticated (following the same cognitive process as themselves) and best responds to this belief. The model nests the standard Level-k and cognitive hierarchy models (when eps = 0) and also Nash behaviour (when eps = 1). Moreover, a sophisticated player with correct beliefs (eps = ps) has best response equal to the winning guess. The model is extended to allow heterogeneity in beliefs. When applied to field data from a guessing game, only 9% of players are estimated to be sophisticated, but these players greatly over-estimate the proportion who are of the same type. This is interpreted as a manifestation of the Dunning-Kruger effect.
Keywords: Beauty contest game; Sophisticated reasoning model; Level k-model; Cognitive hierarchy model; Dunning-Kruger effect. (search for similar items in EconPapers)
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