Unraveling in Guessing Games: An Experimental Study

Description

Consider the following game: a large number of players have to state simultaneously a number in the closed interval [0, 100]. The winner is the person whose chosen number is closest to the mean of all chosen numbers multiplied by a parameter $p$. For $0 \leq p < 1$, the unique Nash equilibrium is zero. This experimental study investigates how players incorporate the behavior of others, focusing on finite depth of reasoning. Experiments were conducted using $p = 1/2, 2/3$, and $4/3$. First-period choices suggest boundedly rational behavior starting from an initial reference point of 50, with clustering around iteration steps 1 and 2 ($50p^n$), accounting for the difference in distributions across parameter values. Over four periods, choices converge toward the equilibrium (0 for $p < 1$, 100 for $p = 4/3$). The modal depth of reasoning does not increase over time. A qualitative learning-direction theory, based on individual experience (adjusting choice direction based on whether the previous adjustment factor was above or below the optimal factor), is proposed as a better explanation for the adjustment process over time than increasing depth of reasoning....