Game Theory in Volleyball
The golden trio of volleyball: Pass, set, spike. The front lines of volleyball teams face an interesting challenge every time their opposing team sets up an attack. Ever since I enrolled in Cornell’s Volleyball PE course and been playing in 6 vs. 6 games, I’ve faced this difficult game theory dilemma. From the receiving pass in the back row, to a well placed middle setter, to a spike in 3 possible directions, my team has a choice to make: where should we defend? Some assumptions that we will have to make along the way are that a spiker will only spike, not tip the ball over, that the ball is “in system,” and the blocker blocks simultaneously to the spiker’s spike. The spiker has the following strategies: spike down the sideline, spike to evade the block, and spike at a sharp angle through the cross court. In response, the defender has the following strategies: block the sideline spike, block the open middle, or block the potential cross court shot.
In a hypothetical payoff matrix, there is no dominant strategy for either spiker nor defender because there is no strategy that would work 100% of the time for either side. If the defender always blocked facing forward to the sideline, the spiker would always successfully evade the block. If the spiker always hits into the open court, the other side will pick up on the pattern and combat that go-to strategy. Also there is no pure Nash equilibrium because there is no overlapping best response as this is a zero-sum game. However it would be necessary to find a mixed Nash equilibrium that could provide a set of possibility formulas to create the most favorable volleyball strategy. Finally, it is equally important to execute the skills of the game better than the other team while also imperative for the spiker to vary the direction of the hits to keep the blockers on their toes. Volleyball players and coaches can follow the mixed strategy formulas to execute at the start of the game and update accordingly based on situational shifts during the game.