OPTIMAL STRATEGIES FOR SOME TEAM GAMES

Consider a game between teams A and B, consisting of a sequence of matches, where each match takes place between one player i from A and one player j from B. Given the probability that player i wins over player j, we investigate optimal strategies on how to choose a player for the next match, for the following two types of team games. The first type assumes that after each match, the loser is eliminated from the list of remaining players, while the winner remains in the list. The team from which all players are eliminated loses the game. Assuming the Bradley-Terry model as the probability model, we first show that the winning probability does not depend on the strategy chosen. It is also shown that the Bradley-Terry model is essentially the only model for which this strategy independence holds. The second type of game assumes that both players are eliminated after each match. In this case, it is shown that choosing a player with equal probability is an optimal strategy in the sense of maximizing the expected number of wins of matches, provided that information about the order of players in the other teams is not available. The case in which a team knows the ordering of the other team is also studied.