Abstract

We study experimentally a two-player game which we find ideal for investigating k-level reasoning. Each player requests an amount of money between 11 and 20 shekels. He receives the amount that he requests and if he requests exactly one shekel less than the other player, he receives an additional 20 shekels. The best response function in this game is straightforward, the k-level strategies are invariant to the two prominent level-0 specifications (randomization or attraction to salience) and the situation calls for self-interest behavior only. Therefore, we propose the game as a test for the "upper bound" for the depth of k-level reasoning in a population. We support this conjecture by studying several variations of the game which manipulate the attractiveness of the level-0 strategy and the monetary cost of undercutting the other player. Keywords: level-k thinking, salience, iterative reasoning..