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We study experimentally a new two-player game: each player requests an amount between 11 and 20 shekels. He receives the requested amount and if he requests exactly one shekel less than the other player, he receives an additional 20 shekels. Level-k reasoning is appealing due to the natural starting point (requesting 20) and the straightforward best-response operation. Nevertheless, almost all subjects exhibit at most three levels of reasoning. Two variants of the game demonstrate that the depth of reasoning is not increased by enhancing the attractiveness of the level-0 strategy or by reducing the cost of undercutting the other player.
Arad et al. (Sat,) studied this question.