The Value of a Draw

A match is a recursive zero-sum game with three possible outcomes: player 1 wins, player 2 wins or there is a draw. We focus on matches whose point games also have three possible outcomes: player 1 scores the point, player 2... [ view full abstract ]

A match is a recursive zero-sum game with three possible outcomes: player 1 wins, player 2 wins or there is a draw. We focus on matches whose point games also have three possible outcomes: player 1 scores the point, player 2 scores the point, or the point is drawn in which case the point game is repeated. We show that a value of a draw can be attached to each state so that an easily-computed stationary equilibrium exists in which players' strategies can be described as minimax behavior in the point games induced by these values.