Talk: Sacha Bourgeois-Gironde (Paris)
Cognitive hierarchy monotony in complex games
It is rather natural to allow for heterogeneity of beliefs in a population of game-players. If this population is not too large - i.e. individual strategies have an infuence on the final outcome of the game - modelling how these heterogenous beliefs keep some level of interdependence and consistency (weaker than the common knowledge of rationality assumption) makes sense. This is, in particular, what is proposed by models of cognitive hierarchies in behavioral game-theory (Camerer, Ho & Chong 2004; Crawford et al. 2013; respectively proposing "cognitive hierarchy theory" - CHT - and "level-k theory"). These models are particulary fit to account for behavior in dominance-solvable games. I will be especially interested, however, in CHT and its extensions to other game structures. How CHT preserves (or not) its main predictive features in complex games such as the Colonel Blotto game and the Lupi (lowest unique positive integer) auction? My main issue will be with what I label "cognitive monotony": the notion that the higher in the hierarchy, given my correct anticipation of the cognitive levels of other players - the better off I am. In other terms, cognitive monotony means that it always pays to be intelligent when intelligence is defined not "autistically" in terms of isolated computing abilities, but in terms of the optimal sensitive to other players cognitive investment in contexts where heterogenous beliefs (and abilities) are at play. Observed best responses in the Lupi auction might undermine cognitive monotony.