We wish to thank Yaniv Ben-Amy and Aviad Shany for research assistance. We are grateful to Anat Bracha, Vincent

Abstract

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 additional 20 shekels. Level-k reasoning is appealing and straightforward here, especially due to the natural starting point (requesting 20) and the simple best-response function. We argue that the game, unlike other familiar games, can serve as a tool for evaluating the "upper bound " of the depth of k-level reasoning in a population. We confirm that the subjects ’ depth of reasoning is not increased by some modifications of the game

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