Empirical Evidence for Mixed Nash Equilibria in One on One Basketball Games
The paper focused on applying Game Theory, specifically a Theorem that focused on entity behavior in games where players play a specific move with (n) probability, where (n) depends upon their opponents probability (p) of playing the same or countering move. In the case of this study, it sought to evaluate how basketball players behavior changed for given changes in (n) and (p), where (n and p) was the probability that the player would drive and the probability that their opponent would defend the drive, and the inverse (n-1, and p-1) was the probability of shooting a jump-shot or defending a jump-shot. The study also sought to examine any possible correlations between player behavior and anthropomorphic variables (height, weight, etc.).
The study showed weak evidence for mixing strategies and for casual correlations between driving and shooting behavior. The study also found weak positive correlations between driving and relative strength and 3/4 spring time, however the sample size and composition makes further research and modeling necessary.
I had the honor of presenting my project at the Works In Progress Symposium at the University Memphis, and plan to present at the National Undergraduate Research Conference, this April. You can learn more about my project and NCUR at the links below: