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Are Behaviours in the "11-20" Game Well Explained by the level-k Model?

Choo, Lawrence C.Y and Kaplan, Todd R. (2014): Are Behaviours in the "11-20" Game Well Explained by the level-k Model?

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We investigate whether behaviours in Arad and Rubinstein (2012) 11-20 game are well explained by the level-k model. We replicate their game in our Baseline experiment and provided two other variations that retain the same mixed-strategy equilibrium but result in different predicted level-k behaviours. Our hypothesis test is motivated by the logic that if the Baseline and variation games capture level-k reasoning behaviours, we should find consistent proportion of level-k types in all games. We considered two types of level-k models where players were assumed to best respond stochastically and found that the level-k models were able to explain the data significantly better than the equilibrium driven alternatives. In addition, the level-k models were also able to demonstrate consistent proportions of level-k types between the differentiated games. Our findings provide support for Arad and Rubinstein (2012) assertion that behaviours in the 11-20 game can be attributed to the level-k models.

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