This post concerns the findings in Nagel (1995). It is a bit outdated but nevertheless still relevant. She examines the Guessing Game, and how individual study-subjects behave in repeated games.
In her paper, she explains the behavior of the study-subjects in two different ways;
- Behavior based on $\bar{X}$ from the previous games.
- Behavior based on individual experience, under the umbrella term Learning-Direction Theory.
Where $\bar{X}$ is the average guess.
She formalizes her claim in the second explanation, in the following way;
\begin{equation} \text{a}_{it}= \begin{cases} \frac{X_{it}}{50}, \text{for } t = 1\\ \frac{X_{it}}{\bar{X}_{t-1}}, \text{for } t = 2,3,4 \end{cases} \end{equation}
Where $a_{it}$ is called the adjustment factor. She then goes on, to define the optimal adjustment factor that comes from retrospective reasoning;
\begin{equation} \text{a}_{opt,t}= \begin{cases} \frac{p\bar{X}_{t}}{50}, \text{for } t = 1\\ \frac{p\bar{X}_{t}}{\bar{X}_{t-1}}, \text{for } t = 2,3,4 \end{cases} \end{equation}
where $p$ is the factor used to adjust the mean. Ie. Guess $\frac{2}{3}$ of Mean.
This claim, is merely a descriptive model that explains how the study-subjects learn. And how they eventually adapt. She finds empirical support from the experiments she makes.
This claim, insofar, is rather simple to grasp and is an important finding.
What I do not understand, is the importance of her first claim. In essence, what she finds is that there is a tendency, as the game is repeated, that the average guess moves towards equilibrium with differing rates depending on $p$.
- How is this even an important finding? This is already the predicted Nash-Equilibrium, albeit, it is reached later than expected.
