“Top, bottom, neutral, defer?” A game theoretic analysis of scholastic wrestling strategy

Abstract

The buzzer rings. Two wrestlers in the midst of an intense match take a pause from their competition with each other after the two minutes of the first period have expired. They look up to the referee to receive instructions about who will have the opportunity to choose the position at the start of the next period. One of the wrestlers is picked after a coin toss and asked by the referee “Top, Bottom, Neutral, or Defer?” In turn, he turns to his coach for guidance on which position he should select. For all the astute advice the coach may be able to give him at the time of this decision, the wrestler would be well-suited to ask a game theorist as well what the optimal strategy for him would be to maximize his payoff in the match. This thesis analyzes the moment of time when a wrestler faces his positioning choice in a match through the lens of game theory, dynamic programming, and statistical analysis. The factors shaping this decision and the outcomes directly emanating from it allow for the creation of a model that effectively evaluates what is the best position to choose based on the score and time remaining in the match.