Depth of Reasoning Models with Sophisticated Agents

Peter Moffatt, Ganna Pogrebna and Graciela Zevallos-Porles
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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.

Abstract: In the context of guessing games, we propose the Sophisticated Reasoning Model (SRM) which includes a “sophisticated†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)
Date: 2020-12
New Economics Papers: this item is included in nep-evo, nep-exp and nep-gth
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