UIL allows questionable ’stacking’ in tennis

Game theory, the idea of choosing between strategies offering different payoffs considering the actions of other players, is a common phenomenon in our lives. We can hardly go through a day without witnessing its ubiquitous effects.

In a dual team tennis match with x players on each team, the ideas of game theory, Nash equilibrium, and pure/mixed strategies become manifest through the art of competitive play. The two coaches of each team devise a lineup beforehand, seeding the players from 1,2,3…x. Often times, coaches are inclined to place their best player at No.1, their second best player at No.2, and so forth. However, a variety of factors including style of play, health conditions, depth of the opponents’ roster, and the perceived competitiveness of the match may frustrate coaches when devising a winning lineup.

When coaches are placed in a situation with little regulation and, optimal probabilities can be obtained by randomizing pure strategies. In their article “…How to form political slates and tennis teams”, Jonathan Hamilton and Richard E. Romano suggest that the best idea is to randomize strategies. For a tennis team, this means that the coach should assign players so that each player on the team has the same probability of playing on the No.1 spot, No.2 spot, etc. The other team sees equal payoffs for all scenarios, as there is an equal chance that any one of the other team’s players could be playing at the No.1 seed. Thus, there is no reason for the coach to choose any particular player himself to play No.1, and the second team chooses to play mixed pure strategies with equal probabilities as well. When this occurs, Hamilton and Romano state that the Nash equilibrium now becomes a mixed strategy with equal probabilities of any match-up, a phenomenon known as “Pure Strategy Equilibrium (PSE)”.

Several instances of PSE have occurred in tennis leagues across the country, as show in the article. The Galveston County Daily News recently reported that several class 4A and 5A high school tennis teams in Texas have removed player numbering in their leagues. Dual team matches “will have the same win 10 individual matches, win the overall dual match concept, but with an added twist-no true lineup.” This new format creates the type of payoff matrix where PSE occurs. Assuming 10 slots for individual player matches, each can choose any combination of players to fill slots 1-10 but they do not know if the other coach is playing Sincere or using some other Insincere combination of players. Thus, there is no incentive with this game format except to randomly select players to fill up the 10 spots.